In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which ...In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which is a class of radial weights satisfying the two-sided doubling conditions.As an application,the bounded and compact positive Toeplitz operators T_(μ,ω)on the endpoint case weighted harmonic Bergman space L_(h,ω)^(1)(D)are characterized.展开更多
In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we char- acterize finite rank commutators and semi-c...In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we char- acterize finite rank commutators and semi-commutators of two Toeplitz operators with quasi- homogeneous symbols.展开更多
In this paper,we study the finite rank product,commutators and semi-commutators of little-Hankel operators with quasihomogeneous symbols on the cutoff harmonic Bergman space b_n^(2).We obtain the conclusions that the ...In this paper,we study the finite rank product,commutators and semi-commutators of little-Hankel operators with quasihomogeneous symbols on the cutoff harmonic Bergman space b_n^(2).We obtain the conclusions that the commutator and semi-commutator of little-Hankel operators with qusihomogeneous symbols are finite rank operators.展开更多
We study zero product problem and finite rank of the Brown-Halmos type results involving products of Toeplitz operators acting on the harmonic Bergman space. We use the Berezin transform and invariant Laplacian in thi...We study zero product problem and finite rank of the Brown-Halmos type results involving products of Toeplitz operators acting on the harmonic Bergman space. We use the Berezin transform and invariant Laplacian in this paper.展开更多
The harmonics that appear in the squirrel cage asynchronous machine have been discussed in great detail in the literature for a long time. However, the systematization of the phenomenon is still pending, so we made an...The harmonics that appear in the squirrel cage asynchronous machine have been discussed in great detail in the literature for a long time. However, the systematization of the phenomenon is still pending, so we made an attempt to fill this gap in the previous parts of our study by elaborating formulas for calculation of parasitic torques. It was a general demand among those who work in this field towards the author to verify his formulas with measurements. In the literature, it seems,only one detailed, purposeful series of measurements has been published so far, the purpose of which was to investigate the effect of the number of rotor slots on the torque-speed characteristic curve of the machine. The main goal of this study is to verify the correctness of the formulas by comparing them with the referred series of measurements. Relying on this, the expected synchronous parasitic torques were developed for the frequently used rotor slot numbers-as a design guide for the engineer.Thus, together with our complete table for radial magnetic pull published in our previous work, the designer has all the principles, data and formulas available for the right number of rotor slots for his given machine and for the drive system. This brings this series of papers to an end.展开更多
Let（M^n, g）（n ≥ 3） be an n-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by R and R？m the scalar curvature and the trace-free Riemannian curvature tensor o...Let（M^n, g）（n ≥ 3） be an n-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by R and R？m the scalar curvature and the trace-free Riemannian curvature tensor of M, respectively. The main result of this paper states that R？m goes to zero uniformly at infinity if for p ≥ n, the L^p-norm of R？m is finite.As applications, we prove that（M^n, g） is compact if the L^p-norm of R？m is finite and R is positive, and（M^n, g） is scalar flat if（M^n, g） is a complete noncompact manifold with nonnegative scalar curvature and finite L^p-norm of R？m. We prove that（M^n, g） is isometric to a spherical space form if for p ≥n/2, the L^p-norm of R？m is sufficiently small and R is positive.In particular, we prove that（M^n, g） is isometric to a spherical space form if for p ≥ n, R is positive and the L^p-norm of R？m is pinched in [0, C）, where C is an explicit positive constant depending only on n, p, R and the Yamabe constant.展开更多
To facilitate rapid analysis of the oscillation stability mechanism in modular multilevel converter-based high voltage direct current(MMC-HVDC)systems and streamline the simulation process for determining MMC impedanc...To facilitate rapid analysis of the oscillation stability mechanism in modular multilevel converter-based high voltage direct current(MMC-HVDC)systems and streamline the simulation process for determining MMC impedance characteristics,a simplified mathematical simulation model for MMC closed-loop impedance is developed using the harmonic state space method.This model considers various control strategies and includes both AC-side and DC-side impedance models.By applying a Nyquist criterion-based impedance analysis method,the stability mechanisms on the AC and DC sides of the MMC are examined.In addition,a data-driven oscillation stability analysis method is also proposed,leveraging a global sensitivity algorithm based on fast model results to identify key parameters influencing MMC oscillation stability.Based on sensitivity analysis results,a parameter adjustment strategy for oscillation suppression is proposed.The simulation results from the MATLAB/Simulinkbased MMC model validate the effectiveness of the proposed method.展开更多
We have constructed the positive definite metric matrixes for the bounded domains of R^n and proved an inequality which is about the Jacobi matrix of a harmonic mapping on a bounded domain of R^n and the metric matrix...We have constructed the positive definite metric matrixes for the bounded domains of R^n and proved an inequality which is about the Jacobi matrix of a harmonic mapping on a bounded domain of R^n and the metric matrix of the same bounded domain.展开更多
A semi-analytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite, fluid-loaded plate is presented. The plate is reinforced with two sets of orthogonally and equall...A semi-analytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite, fluid-loaded plate is presented. The plate is reinforced with two sets of orthogonally and equally spaced beam stiffeners, which are assumed to be line forces. The response of the stiffened plate to a convected harmonic pressure in the wave-number space is obtained by adopting the Green＇s function and Fourier transform methods. Using the boundary conditions and space harmonic method, we establish the relationship between the stiffener forces and the vibration displacement of the plate. In this paper, the stiffener forces are expressed in terms of harmonic amplitudes of the plate displacement, which are calculated by using a numerical reduction technique. Finally, the Fourier inverse transform is employed to find expressions of the vibration and sound radiation in physical space. Agreements with existing results prove the validity of this approach and more numerical results are presented to show that this method converges rapidly.展开更多
We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■...We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■ and ψ satisfy one of the following conditions:(1) Both ■ and ψ are analytic on D.(2) Both ■ and ψ are anti-analytic on D.(3) There exist complex constants α and β, not both 0, such that ■ = αψ + β.Furthermore, we give the necessary and sufficient conditions for S■Sψ= S■ψ.展开更多
Line commutated converter based high-voltage direct-current(LCC-HVDC)transmissions are prone to harmonic oscillation under weak grids.Impedance modeling is an effective method for assessing interaction stability.First...Line commutated converter based high-voltage direct-current(LCC-HVDC)transmissions are prone to harmonic oscillation under weak grids.Impedance modeling is an effective method for assessing interaction stability.Firstly,this paper proposes an improved calculation method for the DC voltage and AC currents of commutation stations to address the complex linearization of the commutation process and constructs an overall harmonic state-space(HSS)model of an LCC-HVDC.Based on the HSS model,the closed-loop AC impedances on the LCC-HVDC sending and receiving ends are then derived and verified.The impedance characteristics of the LCC-HVDC are then analyzed to provide a physical explanation for the harmonic oscillation of the system.The effects of the grid strength and control parameters on system stability are also analyzed.To improve the impedance characteristics and operating stability of the LCC-HVDC system,a virtual impedance based stability enhancement control is proposed,and a parameter design method is considered to ensure satisfactory phase margins at both the sending and receiving ends.Finally,simulation results are presented to verify the validity of the impedance model and virtual impedance based stability enhancement control.展开更多
In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We sol...In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.展开更多
In this paper, we characterize the symbols for （semi-）commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on （Dh）⊥ if...In this paper, we characterize the symbols for （semi-）commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on （Dh）⊥ if and only if φ and ψ satisfy one of the following conditions： （1） Both φ and ψ are harmonic functions; （2） There exist complex constants α and β, not both O, such that φ = αφ＋β.展开更多
In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal...In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal.Then we obtain a necessary and sufficient condition for the dual Toeplitz operator S_(φ) with the symbol φ(z)=az^(n1zm1)+bz^(n2zm2)(n1,n2,m1,m2∈N and a,b∈C)to be hyponormal.Finally,we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a finite rank.展开更多
In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the ...In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator.展开更多
In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
In this paper,we characterize that the boundedness,compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic Bergman space.This generalizes the corresponding res...In this paper,we characterize that the boundedness,compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic Bergman space.This generalizes the corresponding results for dual Toeplitz operators on the orthogonal complement of the Bergman space due to Stroethoff and Zheng’s paper[Trans.Amer.Math.Soc.,354,2495–2520(2002)].展开更多
Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of...Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.展开更多
The quantization of circuits has received to be rather attractive in domains of solid state—molecular—and biophysics, since the quanta referred to as Q-bits play a significant role in the design of the quantum compu...The quantization of circuits has received to be rather attractive in domains of solid state—molecular—and biophysics, since the quanta referred to as Q-bits play a significant role in the design of the quantum computer and entangled structures. Quantized circuits cannot be applied without modifications, since the energy differences are not equidistant and the polarization of the excited states has to be accounted for having particular importance for the creation of virtual states. Applications of the presented theory are scanning methods in radiotherapy without multi-leaf collimators, which may be realized in tomo-scanning radiotherapy and in the keV domain, which provides a new design of CT. The problem of lateral scatter in the target and energy storage by heat production is significantly reduced by a multilayer system with focusing the impinging electrons at the walls and by a magnetic field. The verification of the Heisenberg-Euler scatter of crossing beams of 9 MV is a central problem of photon physics and can be solved by the new bremsstrahlung technique. A comparison with GEANT 4 Monte-Carlo data indicates that the presented method also works in the GeV domain, and a multi-target can improve the bremsstrahlung yield. GEANT 4 provides the spatial distribution, whereas the virtual oscillator states only show the created energy spectrum. In every case, the exploitation yield can be drastically improved by the superiority of the focused multitarget system compared to a single standard target, and the door to new technologies is opened.展开更多
In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not h...In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .展开更多
基金supported by the National Natural Science Foundation of China(12171075)the Science and Technology Research Project of Education Department of Jilin Province(JJKH20241406KJ)Zhan’s research was supported by the Doctoral Startup Fund of Liaoning University of Technology(XB2024029).
文摘In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which is a class of radial weights satisfying the two-sided doubling conditions.As an application,the bounded and compact positive Toeplitz operators T_(μ,ω)on the endpoint case weighted harmonic Bergman space L_(h,ω)^(1)(D)are characterized.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1127105911301047)the Scientific Research Found of Higher School of Inner Mongolia(Grant No.NJZY 13298)
文摘In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we char- acterize finite rank commutators and semi-commutators of two Toeplitz operators with quasi- homogeneous symbols.
基金Supported by the National Natural Science Foundation of China(Grant No.11761006)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(Grant No.2021MS01002)Program for Young Talents of Chifeng University(Grant No.CFXYYT2201)。
文摘In this paper,we study the finite rank product,commutators and semi-commutators of little-Hankel operators with quasihomogeneous symbols on the cutoff harmonic Bergman space b_n^(2).We obtain the conclusions that the commutator and semi-commutator of little-Hankel operators with qusihomogeneous symbols are finite rank operators.
基金Supported by the National Natural Science Foundation of China(Grant No.11671065)
文摘We study zero product problem and finite rank of the Brown-Halmos type results involving products of Toeplitz operators acting on the harmonic Bergman space. We use the Berezin transform and invariant Laplacian in this paper.
文摘The harmonics that appear in the squirrel cage asynchronous machine have been discussed in great detail in the literature for a long time. However, the systematization of the phenomenon is still pending, so we made an attempt to fill this gap in the previous parts of our study by elaborating formulas for calculation of parasitic torques. It was a general demand among those who work in this field towards the author to verify his formulas with measurements. In the literature, it seems,only one detailed, purposeful series of measurements has been published so far, the purpose of which was to investigate the effect of the number of rotor slots on the torque-speed characteristic curve of the machine. The main goal of this study is to verify the correctness of the formulas by comparing them with the referred series of measurements. Relying on this, the expected synchronous parasitic torques were developed for the frequently used rotor slot numbers-as a design guide for the engineer.Thus, together with our complete table for radial magnetic pull published in our previous work, the designer has all the principles, data and formulas available for the right number of rotor slots for his given machine and for the drive system. This brings this series of papers to an end.
基金Supported by the National Natural Science Foundations of China(Grant Nos.1126103811361041)the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB201005)
文摘Let（M^n, g）（n ≥ 3） be an n-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by R and R？m the scalar curvature and the trace-free Riemannian curvature tensor of M, respectively. The main result of this paper states that R？m goes to zero uniformly at infinity if for p ≥ n, the L^p-norm of R？m is finite.As applications, we prove that（M^n, g） is compact if the L^p-norm of R？m is finite and R is positive, and（M^n, g） is scalar flat if（M^n, g） is a complete noncompact manifold with nonnegative scalar curvature and finite L^p-norm of R？m. We prove that（M^n, g） is isometric to a spherical space form if for p ≥n/2, the L^p-norm of R？m is sufficiently small and R is positive.In particular, we prove that（M^n, g） is isometric to a spherical space form if for p ≥ n, R is positive and the L^p-norm of R？m is pinched in [0, C）, where C is an explicit positive constant depending only on n, p, R and the Yamabe constant.
基金National Natural Science Foundation of China(52307127)State Key Laboratory of Power System Operation and Control(SKLD23KZ07)。
文摘To facilitate rapid analysis of the oscillation stability mechanism in modular multilevel converter-based high voltage direct current(MMC-HVDC)systems and streamline the simulation process for determining MMC impedance characteristics,a simplified mathematical simulation model for MMC closed-loop impedance is developed using the harmonic state space method.This model considers various control strategies and includes both AC-side and DC-side impedance models.By applying a Nyquist criterion-based impedance analysis method,the stability mechanisms on the AC and DC sides of the MMC are examined.In addition,a data-driven oscillation stability analysis method is also proposed,leveraging a global sensitivity algorithm based on fast model results to identify key parameters influencing MMC oscillation stability.Based on sensitivity analysis results,a parameter adjustment strategy for oscillation suppression is proposed.The simulation results from the MATLAB/Simulinkbased MMC model validate the effectiveness of the proposed method.
基金Supported by the Tianyuan Foundation(A0324609)Supported by the research grant, of Beijing Municipal Government
文摘We have constructed the positive definite metric matrixes for the bounded domains of R^n and proved an inequality which is about the Jacobi matrix of a harmonic mapping on a bounded domain of R^n and the metric matrix of the same bounded domain.
基金Project supported by the National Natural Science Foundation of China (Nos. 05475150,50875030,10872039 and 90816025)
文摘A semi-analytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite, fluid-loaded plate is presented. The plate is reinforced with two sets of orthogonally and equally spaced beam stiffeners, which are assumed to be line forces. The response of the stiffened plate to a convected harmonic pressure in the wave-number space is obtained by adopting the Green＇s function and Fourier transform methods. Using the boundary conditions and space harmonic method, we establish the relationship between the stiffener forces and the vibration displacement of the plate. In this paper, the stiffener forces are expressed in terms of harmonic amplitudes of the plate displacement, which are calculated by using a numerical reduction technique. Finally, the Fourier inverse transform is employed to find expressions of the vibration and sound radiation in physical space. Agreements with existing results prove the validity of this approach and more numerical results are presented to show that this method converges rapidly.
基金supported by National Natural Science Foundation of China(Grant Nos.10971020 and 1127059)Research Fund for the Doctoral Program of Higher Education of China
文摘We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■ and ψ satisfy one of the following conditions:(1) Both ■ and ψ are analytic on D.(2) Both ■ and ψ are anti-analytic on D.(3) There exist complex constants α and β, not both 0, such that ■ = αψ + β.Furthermore, we give the necessary and sufficient conditions for S■Sψ= S■ψ.
基金supported in part by the National Natural Science Foundation of China(No.U2166602)in part by the Major Special Project of Hunan Province(No.2020GK1010)in part by the Innovation Young Talents Program of Changsha Science and Technology Bureau(No.kq2107005).
文摘Line commutated converter based high-voltage direct-current(LCC-HVDC)transmissions are prone to harmonic oscillation under weak grids.Impedance modeling is an effective method for assessing interaction stability.Firstly,this paper proposes an improved calculation method for the DC voltage and AC currents of commutation stations to address the complex linearization of the commutation process and constructs an overall harmonic state-space(HSS)model of an LCC-HVDC.Based on the HSS model,the closed-loop AC impedances on the LCC-HVDC sending and receiving ends are then derived and verified.The impedance characteristics of the LCC-HVDC are then analyzed to provide a physical explanation for the harmonic oscillation of the system.The effects of the grid strength and control parameters on system stability are also analyzed.To improve the impedance characteristics and operating stability of the LCC-HVDC system,a virtual impedance based stability enhancement control is proposed,and a parameter design method is considered to ensure satisfactory phase margins at both the sending and receiving ends.Finally,simulation results are presented to verify the validity of the impedance model and virtual impedance based stability enhancement control.
基金Supported by National Natural Science Foundation of China(Grant No.11271059)
文摘In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.
基金Supported by NSFC(Grant Nos.11271059,11271332,11431011,11301047)NSF of Zhejiang Province(Grant Nos.LY14A010013,LY14A010021)Higher School Foundation of Inner Mongolia of China(Grant No.NJZY13298)
文摘In this paper, we characterize the symbols for （semi-）commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on （Dh）⊥ if and only if φ and ψ satisfy one of the following conditions： （1） Both φ and ψ are harmonic functions; （2） There exist complex constants α and β, not both O, such that φ = αφ＋β.
基金Partially supported by NSFC(Grant No.11701052)the second author was partially supported by the Fundamental Research Funds for the Central Universities(Grant Nos.2020CDJQY-A039 and 2020CDJ-LHSS-003)。
文摘In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal.Then we obtain a necessary and sufficient condition for the dual Toeplitz operator S_(φ) with the symbol φ(z)=az^(n1zm1)+bz^(n2zm2)(n1,n2,m1,m2∈N and a,b∈C)to be hyponormal.Finally,we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a finite rank.
基金Supported by NSFC(Grant No.11271387)Chongqing Natural Sience Foundation(Grant No.cstc2013jjB0050)
文摘In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator.
基金Supported by Tianyuan Funds of China (Grant No. 10926143)YSF of Shanxi Province (Grant No. 20100210022)+1 种基金partially supported by NSFC (Grant No. 10971195)NSF of Zhejiang Province (Grant Nos. Y6090689, Y6110260)
文摘In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
基金Supported by NSFC(Grant No.11701052)Fundamental Research Funds for the Central Universities(Grant Nos.106112017CDJXY100007,2020CDJQY-A039,2020CDJ-LHSS-003)。
文摘In this paper,we characterize that the boundedness,compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic Bergman space.This generalizes the corresponding results for dual Toeplitz operators on the orthogonal complement of the Bergman space due to Stroethoff and Zheng’s paper[Trans.Amer.Math.Soc.,354,2495–2520(2002)].
基金supported by the National Natural Science Foundation of China(Nos.11101139,11271124)the Natural Science Foundation of Zhejiang Province(Nos.Y6090036,Y6100219)the Foundation of Creative Group in Universities of Zhejiang Province(No.T200924)
文摘Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.
文摘The quantization of circuits has received to be rather attractive in domains of solid state—molecular—and biophysics, since the quanta referred to as Q-bits play a significant role in the design of the quantum computer and entangled structures. Quantized circuits cannot be applied without modifications, since the energy differences are not equidistant and the polarization of the excited states has to be accounted for having particular importance for the creation of virtual states. Applications of the presented theory are scanning methods in radiotherapy without multi-leaf collimators, which may be realized in tomo-scanning radiotherapy and in the keV domain, which provides a new design of CT. The problem of lateral scatter in the target and energy storage by heat production is significantly reduced by a multilayer system with focusing the impinging electrons at the walls and by a magnetic field. The verification of the Heisenberg-Euler scatter of crossing beams of 9 MV is a central problem of photon physics and can be solved by the new bremsstrahlung technique. A comparison with GEANT 4 Monte-Carlo data indicates that the presented method also works in the GeV domain, and a multi-target can improve the bremsstrahlung yield. GEANT 4 provides the spatial distribution, whereas the virtual oscillator states only show the created energy spectrum. In every case, the exploitation yield can be drastically improved by the superiority of the focused multitarget system compared to a single standard target, and the door to new technologies is opened.
基金supported by National Natural Science Foundation of China(Grant No.11271387)Chongqing Natural Sience Foundation(Grant No.2013jjB 0050)Simons Foundation(Grant No.196300)
文摘In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .
