In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces？∞, c and c0 according to a new matrix operator W which is obtained by matrix pr...In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces？∞, c and c0 according to a new matrix operator W which is obtained by matrix product.展开更多
In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1....In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1. The product operator G （u, v; △） over l1 is defined by （G（u,v;△）x）k=^k∑i=0ukvi（xi- xi-1） with xk = 0 for all k 〈 0, where x = （xk）∈e1,and u and v axe either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G （u, v; △） on the sequence space gl.展开更多
The operator equation λMz^-X = XMzk, for k ≥ 2,λ∈ C, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.
A problem of nanocatalyst improvement is considered. The existence of irregularities at the surface of nanoparticle leads to the increasing of the surface/volume ratio and, correspondingly, to the improvement of the c...A problem of nanocatalyst improvement is considered. The existence of irregularities at the surface of nanoparticle leads to the increasing of the surface/volume ratio and, correspondingly, to the improvement of the catalytic activity. But this impurity gives one an additional effect due to the change of the electronic density at the surface. We suggest simple model for the description of this effect. The model allows one to find the discrete spectrum of the Schrdinger operator for nanoparticle. Due to this impurity induced bound states the electron density increases near the surface. It leads to the increase of the catalytic activity of nanoparticles with surface impurities.展开更多
The author considers the embedding problem of weighted Sobolev spaces H<sup>n</sup><sub>p</sub> in weighted L<sub>s</sub> spaces L<sub>s,r</sub>,and some sufficient cond...The author considers the embedding problem of weighted Sobolev spaces H<sup>n</sup><sub>p</sub> in weighted L<sub>s</sub> spaces L<sub>s,r</sub>,and some sufficient conditions and necessary conditions are given, when weight functions satisfy certain conditions.The author uses the results obtained to the qualitative analysis of the spectrum of 2n-order weighted differential operator,and gives some sufficient conditions and necessary conditions to ensure that the spectrum is discrete.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
The sequence space bvp consisting of all sequences （xk） such that （xk -xk-1） belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55（1）, 136-147（2003）]; where 1 ≤ p ≤ ...The sequence space bvp consisting of all sequences （xk） such that （xk -xk-1） belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55（1）, 136-147（2003）]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg＇s classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.展开更多
文摘In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces？∞, c and c0 according to a new matrix operator W which is obtained by matrix product.
文摘In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1. The product operator G （u, v; △） over l1 is defined by （G（u,v;△）x）k=^k∑i=0ukvi（xi- xi-1） with xk = 0 for all k 〈 0, where x = （xk）∈e1,and u and v axe either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G （u, v; △） on the sequence space gl.
文摘The operator equation λMz^-X = XMzk, for k ≥ 2,λ∈ C, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.
基金Supported by Federal Targeted Program "Scientific and Educational Human Resources for Innovation-Driven Russia" (contracts P689NK-526P, 14.740.11.0879, and 16.740.11.0030) and grant 11-08-00267 of Russian Foundation for Basic Researchesstate contract SC16.516.11.6073 and by Federal Targeted Program "Researches and Development in the Prioring Directions Developments of a Scientific and Technological Complex of Russia 2007-2013" (state contract 07.514.11.4146)
文摘A problem of nanocatalyst improvement is considered. The existence of irregularities at the surface of nanoparticle leads to the increasing of the surface/volume ratio and, correspondingly, to the improvement of the catalytic activity. But this impurity gives one an additional effect due to the change of the electronic density at the surface. We suggest simple model for the description of this effect. The model allows one to find the discrete spectrum of the Schrdinger operator for nanoparticle. Due to this impurity induced bound states the electron density increases near the surface. It leads to the increase of the catalytic activity of nanoparticles with surface impurities.
基金Supported by the National Natural Science Fundation of Chinathe Natural Science Foundation of Inner Mongolia.
文摘The author considers the embedding problem of weighted Sobolev spaces H<sup>n</sup><sub>p</sub> in weighted L<sub>s</sub> spaces L<sub>s,r</sub>,and some sufficient conditions and necessary conditions are given, when weight functions satisfy certain conditions.The author uses the results obtained to the qualitative analysis of the spectrum of 2n-order weighted differential operator,and gives some sufficient conditions and necessary conditions to ensure that the spectrum is discrete.
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 .
文摘The sequence space bvp consisting of all sequences （xk） such that （xk -xk-1） belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55（1）, 136-147（2003）]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg＇s classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.
