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ON GRAPH MEASURES IN BANACH SPACES AND DESCRIPTION OF essential spectra OF MULTIDIMENSIONAL TRANSPORT EQUATION

Acta Mathematica Scientia 2012年第5期32卷 2050-2064页

作者： Boulbeba Abdelmoumen Aref Jeribi Maher Mnif Dpartement de Mathmatiques Universit de SfaxFacult des Sciences de SfaxRoute de SoukraKm 3.5B.P.11713000SfaxTunisie

In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak ***,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach *** results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.

关键词： measures of noncompactness and weak noncompactness in Banach spaces Fredholm operators essential spectra

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Browder spectra and essential spectra of Operator Matrices

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Acta Mathematica Sinica,English Series 2008年第6期24卷 947-954页

作者： Yun Nan ZHANG Huai Jie ZHONG Li Qiong LIN Department of Mathematics Xiamen University Xiamen 351005 P. R. China School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 P. R. China College of Mathematics and Computer Science Fuzhou University Fuzhou 350002 P. R. China

Let Mc = （ A0CB ） be a 2 × 2 upper triangular operator matrix acting on the Banach space X × Y. We prove that σr（A） ∪ σr（ B）= σr （Mc） ∪ W ,where W is the union of certain of the holes in σr（Mc） which happen to be subsets of σr（A） ∩ σr（B）, and σr（A）, σr（B）, σr（Mc） can be equal to the Browder or essential spectra of A, B, Mc, respectively. We also show that the above result isn＇t true for the Kato spectrum, left （right） essential spectrum and left （right） spectrum.

关键词： Banach space operator matrices Browder spectra essential spectra

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On the spectra of General Ordinary Quasi-Differential Operators and Their L²_w-Solutions

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Advances in Pure Mathematics 2022年第3期12卷 186-205页

作者： Sobhy El-Sayed Ibrahim Department of Mathematics Faculty of Basic Education Public Authority of Applied Education and Training Kuwait City Kuwait

In this paper, we consider the general ordinary quasi-differential expression τ of order n with complex coefficients and its formal adjoint τ+ on the interval [a,b). We shall show in the case of one singular end-point and under suitable conditions that all solutions of a general ordinary quasi-differential equation are in the weighted Hilbert space provided that all solutions of the equations and its adjoint are in . Also, a number of results concerning the location of the point spectra and regularity fields of the operators generated by such expressions may be obtained. Some of these results are extensions or generalizations of those in the symmetric case, while the others are new.

关键词： General Ordinary Quasi-Differential Expressions Regular and Singular End-Points Singular Differential Operators essential spectra Point spectra and Regularity Fields

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spectra of the Energy Operator of Two-Electron System in the Impurity Hubbard Model

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Journal of Applied Mathematics and Physics 2022年第9期10卷 2743-2779页

作者： Sa’dulla Tashpulatov Laboratory Physics of Multiparticle Systems Institute of Nuclear Physics of the Academy of Sciences of the Republic of Uzbekistan Tashkent Uzbekistan

We consider two-electron systems for the impurity Hubbard Model and investigate the spectrum of the system in a singlet state for the v-dimensional integer valued lattice Zv. We proved the essential spectrum of the system in the singlet state is consists of union of no more then three intervals, and the discrete spectrum of the system in the singlet state is consists of no more then five eigenvalues. We show that the discrete spectrum of the system in the triplet and singlet states differ from each other. In the singlet state the appear additional two eigenvalues. In the triplet state the discrete spectrum of the system can be empty set, or is consists of one-eigenvalue, or is consists of two eigenvalues, or is consists of three eigenvalues. For investigation the structure of essential spectra and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of two-electron systems in an impurity Hubbard model.

关键词： Two-Electron System Impurity Hubbard Model Singlet State Triplet State essential spectra Discrete Spectrum

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Multipliers on the Dirichlet Space for the Annulus

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Journal of Mathematical Research with Applications 2018年第2期38卷 169-182页

作者： Zelong CAO Junlin LIU Li HE Zhixin High School Department of Mathematics Guangzhou University

Multipliers on the classic Dirichlet space of the unit disk are much more complex than those on the Hardy space and the Bergman space, many basic problems have not been solved, such as the boundedness, which is still an open problem. The annulus, as a kind of typical complex connected domain, has more complicated function structure. This paper focuses on discussing the invertibility and Fredholmness of multipliers on the Dirichlet space of the annulus. The spectra and essential spectra of multipliers with Laurent polynomials symbols are calculated. In addition, we anwser a problem proposed by Guangfu CAO and Li HE on spectrum and essential spectrum for general multipliers.

关键词： annulus multiplier spectra essential spectra

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