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The essential spectrum and Banach Reducibility of Operator Weighted Shifts

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Acta Mathematica Sinica,English Series 2001年第3期17卷 413-424页

作者： Jue Xian LI Department of Mathematics,Jilin University,Changchun 130023,P.R.China Department of Mathematics.Liaoning University.Shenyang 110036.P.R.China E-mail:Lixli@263.netYou Qing JI Shan Li SUN Departmerit of Mathematics.Jilin University,Changchun 130023.P.R.China Department of Mathematics Jilin University Changchun 130023 P. R. China Department of Mathematics Liaoning University Shenyang 110036 P. R. China

For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are ***,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Douglas operator ... 详细信息

关键词： Operator weighted shift essential spectrum Banach reducibility Cowen-Douglas operator

Bifurcation from the essential spectrum for an elliptic equation with general nonlinearities

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Science China Mathematics 2023年第10期66卷 2243-2260页

作者： Jianjun Zhang Xuexiu Zhong Huansong Zhou College of Mathematics and Statistics Chongqing Jiaotong UniversityChongqing 400074China South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China Center for Mathematical Sciences and Department of Mathematics Wuhan University of TechnologyWuhan 430070China

In this paper,based on some prior estimates,we show that the essential spectrum λ=0 is a bifurcation point for a superlinear elliptic equation with only local conditions,which generalizes a series of earlier results ... 详细信息

关键词： elliptic equation bifurcation point essential spectrum

ON THE essential spectrum OFPSEUDODIFFERENTIAL OPERATORS (II)

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Chinese Annals of Mathematics,Series B 1994年第3期15卷 327-334页

作者： FAN QIRONG(Institute & Department of Mathematics, Beijing Unversity) Beijing 100071, China.)

This paper continues the studies of the essential spectrum Of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativisticSchredinger operator, ￣ + v(x), co... 详细信息

关键词： essential spectrum Pseudodifferelltial operator Schrsdiliger operator.

Structure of essential spectrum and Discrete Spectra of the Energy Operator of Five-Electron Systems in the Hubbard Model. Third and Fourth Doublet States

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Journal of Applied Mathematics and Physics 2020年第12期8卷 2886-2918页

作者： S. M. Tashpulatov Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider a five-electron system in the Hubbard model with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in the third and fourth doublet states in a v-dimensional lattice is investigated. We prove that the essential spectrum of the system in a third doublet state consists is the union of at most four segments, and discrete spectrum of the system is empty. We show that the essential spectrum of the system in a fourth doublet state consists of the union of at most seven segments, and discrete spectrum of the system consists of no more than one point.

关键词： essential spectrum Discrete spectrum Five-Electron System Bound State Anti-Bound State Hubbard Model Doublet State Sextet State Quartet State

Structure of essential Spectra and Discrete spectrum of the Energy Operator of Six-Electron Systems in the Hubbard Model. First Quintet and First Singlet States

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Journal of Applied Mathematics and Physics 2022年第11期10卷 3424-3461页

作者： S. M. Tashpulatov Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider the energy operator of six-electron systems in the Hubbard model and investigate the structure of essential spectra and discrete spectrum of the system in the first quintet and first singlet states in the ... 详细信息

关键词： Hubbard Model essential spectrum Discrete spectrum Six Electron Systems Octet State Singlet State Quintet State

The Structure of essential Spectra and Discrete spectrum of Three-Electron Systems in the Impurity Hubbard Model—Quartet State

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Journal of Applied Mathematics and Physics 2021年第6期9卷 1391-1421页

作者： S. M. Tashpulatov Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider a three-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy operator of three-electron systems in the impurity Hubbard model in the quartet state of the system in a v-dimensional lattice. We have reduced the study of the spectrum of the three-electron quartet state operator in the impurity Hubbard model to the study of the spectrum of a simpler operator. We proved the essential spectra of the three-electron systems in the Impurity Hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues.

关键词： essential spectrum Discrete spectrum Three-Electron System Local Impurity States Impurity Hubbard Model Quartet State Doublet State

Criteria for Discrete spectrum of 1D Operators

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Communications in Mathematics and Statistics 2014年第3期2卷 279-309页

作者： Mu-Fa Chen School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex Systems(Beijing Normal University)Ministry of EducationBeijing 100875People’s Republic of China

For discrete spectrum of 1D second-order differential/difference operators(with or without potential(killing),with the maximal/minimal domain),a pair of unified dual criteria are presented in terms of two explicit measures and the harmonic function of the ***,these criteria can be read out from the ones for the exponential convergence of four types of stability studied earlier,simply replacing the‘finite supremum’by‘vanishing at infinity’.Except a dual technique,the main tool used here is a transform in terms of the harmonic function,to which two new practical algorithms are introduced in the discrete context and two successive approximation schemes are reviewed in the continuous *** of them are illustrated by *** main body of the paper is devoted to the hard part of the story,the easier part but powerful one is delayed to the end of the paper.

关键词： Discrete spectrum essential spectrum Tridiagonal matrix(birth–death process) Second-order differential operator(diffusion) Killing

Super and Weak Poincare Inequalities for Hypoelliptic Operators

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Acta Mathematicae Applicatae Sinica 2009年第4期25卷 617-630页

作者： Feng-yu Wangt School of Mathematical Sciences and Lab. Math. Com. Sys. Beijing Normal University Beijing 100875 China Department of Mathematics Swansea University Singleton Park SA2 8PP Swansea UK

Sufficient conditions are presented for super/weak Poincare inequalities to hold for a class of hypoelliptic operators on noncompact manifolds. As applications, the essential spectrum and the convergence rate of the associated Markov semigroup are described for Gruschin type operators on R2 and Kohn-Laplacian type operators on the Heisenberg group.

关键词： Hypoelliptic operator super Poincare inequality essential spectrum weak Poincar~ inequality

MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

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Acta Mathematica Scientia 2013年第5期33卷 1463-1470页

作者： B.YOUSEFI Sh.KHOSHDEL Y.JAHANSHAHI Department of Mathematics Payame Noor University

Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.

关键词： invariant subspace Hilbert space of analytic functions essential spectrum essential norm Fredholm operator multiplication operator