In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the repr...In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.展开更多
Based on the conclusion that the generalized Bargmann representation of a two-mode Fock state is a two-variable Hermite polynomial function /Hong-Yi Fan and Jun-hua Chen,Phys.Lett.A303(2002)311] we derive the generali...Based on the conclusion that the generalized Bargmann representation of a two-mode Fock state is a two-variable Hermite polynomial function /Hong-Yi Fan and Jun-hua Chen,Phys.Lett.A303(2002)311] we derive the generalized Bargmann representation of the spin coherent state and some new relations in the generalized function space.展开更多
In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In additio...In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.展开更多
In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax ...In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax pair under the Bargmann constraint. It is also shown that the potential u in the stationary Sehrodinger equation can be a summation of squares of wave functions from bilinear point of view.展开更多
We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles： local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark＇s uncert...We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles： local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark＇s uncertainty principle and Matolcsi-Sz^ics uncertainty principle.展开更多
基金Supported by NSFC(No.12001482)Innovative Guidance Project of Science and Technology of Zhaoqing City(Nos.202004031503,202004031505)+2 种基金Scientific Research Ability Enhancement Program for Excellent Young Teachers of Zhaoqing University(No.ZQ202108)Natural Research Project of Zhaoqing University(Nos.221622,KY202141,201910)Innovative Research Team Project of Zhaoqing University。
文摘In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.
文摘Based on the conclusion that the generalized Bargmann representation of a two-mode Fock state is a two-variable Hermite polynomial function /Hong-Yi Fan and Jun-hua Chen,Phys.Lett.A303(2002)311] we derive the generalized Bargmann representation of the spin coherent state and some new relations in the generalized function space.
基金Supported by the National Natural Science Foundation of China(Grant No.11271092)the Natural Science Foundation of Guangdong Province(Grant No.S2011010005367)
文摘In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10871165 and 10671121
文摘In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax pair under the Bargmann constraint. It is also shown that the potential u in the stationary Sehrodinger equation can be a summation of squares of wave functions from bilinear point of view.
文摘We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles： local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark＇s uncertainty principle and Matolcsi-Sz^ics uncertainty principle.
