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 &...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 <em>v</em>-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.展开更多
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 ...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 on an open problem proposed by Stuart(1983).展开更多
This paper gives characterizations for diffusion processes on the line and birth-death processes whose generators admit the empty essential spectra. Some equivalent conditions for empty essential spectra for general M...This paper gives characterizations for diffusion processes on the line and birth-death processes whose generators admit the empty essential spectra. Some equivalent conditions for empty essential spectra for general Markov generators are also discussed.展开更多
For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Do...For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Douglas operator is characterized.展开更多
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...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 <em>v</em>-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.展开更多
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...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), complete results are obtained.展开更多
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 ...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 v-dimensional lattice.展开更多
In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we es...In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter＇s and approximate essential spectrum.展开更多
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...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,...,＋∞}.展开更多
We consider the energy operator of four-electron systems in an impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensi...We consider the energy operator of four-electron systems in an impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensional lattice. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-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 four-electron systems in an impurity Hubbard model. The investigations show that there are such cases: 1) the essential spectrum of the system consists of the union of no more than eight segments, and the discrete spectrum of the system consists of no more than three eigenvalues;2) the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues;3) the essential spectrum of the system consists of the union of no more than three segments, and the discrete spectrum of the system is the empty set. Consequently, the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.展开更多
In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of clos...In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of closed densely defined linear operators on Banach spaces.展开更多
An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(...An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.展开更多
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 mea...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 operators.Interestingly,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 context.All of them are illustrated by examples.The 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.展开更多
When A ∈ B（H） and B ∈ B（K） are given, we denote by Me the operator matrix acting on the infinite dimensional separable Hilbert space H ＋ K of the form Me = （ A C O B）. In this paper, a necessary and sufficien...When A ∈ B（H） and B ∈ B（K） are given, we denote by Me the operator matrix acting on the infinite dimensional separable Hilbert space H ＋ K of the form Me = （ A C O B）. In this paper, a necessary and sufficient condition for Me to be left Fredholm for some C ∈ F（K, H） （C ∈ Inv（K, H）） is given, where F（K,H） and Inv（K, H） denote respectively, the set of Fredholm operators and the set of invertible operators of B（K, H）. In addition, we give a necessary and sufficient condition for Me to be left Fredholm for all C ∈ Inv（K, H）.展开更多
This paper discusses the connectivity of the essential spectra of Toeplitz operators with symbols in H∞ +C on Hardy spaces and weighted Bergman spaces for several complex variables.
Let MX=（A C X B ）be a 2×2 operator matrix acting on the Hilbert space H＋K. For given A∈B（H）,B∈B（K）and C∈B（K,H）the set UX∈B（H,K）^σe（MX）is determined, whereσe（T）denotes the essential spectrum.
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 a...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.展开更多
This paper presents the analysis of exponential stability of a system consisting of a robot and its associated safety mechanism. The system have various modes of failures and is repairable. The paper investigates the ...This paper presents the analysis of exponential stability of a system consisting of a robot and its associated safety mechanism. The system have various modes of failures and is repairable. The paper investigates the nonnegative stead-state solution of system,the existence of strictly dominant eigenvalue and restriction of essential spectrum growth bound of the system operator. The essential spectral radius of the system operator is also discussed before and after perturbation. The results show that the dynamic solution of the system is exponential stab＇flity and converges to the steady-state solution.展开更多
The paper presents a model of a redundant robot configuration with a built-in safety. By the method of strong continuous semi-group, the paper analyzes the essential spectrum of the system operator before and after pe...The paper presents a model of a redundant robot configuration with a built-in safety. By the method of strong continuous semi-group, the paper analyzes the essential spectrum of the system operator before and after perturbation. The results show that in s special condition, the dynamic solution of the system is exponential stability and tends to the steady solution of the system.展开更多
文摘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 <em>v</em>-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.
基金supported by National Natural Science Foundation of China(Grant Nos.11801581,11871123,11931012 and 12271184)Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2021A1515010034 and 2018A030310082)+2 种基金Guangzhou Association for Science and Technology(Grant No.202102020225)Chongqing Science and Technology Bureau(Grant No.JDDSTD201802)Chongqing University Science Foundation(Grant No.CXQT21021).
文摘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 on an open problem proposed by Stuart(1983).
基金Research supported in part by RFDP(No.2001002707)973 ProjectNSFC(No.10121101)
文摘This paper gives characterizations for diffusion processes on the line and birth-death processes whose generators admit the empty essential spectra. Some equivalent conditions for empty essential spectra for general Markov generators are also discussed.
基金Supported by MCME.Doctoral Foundation of the Ministry of Education and Science Foundation of Liaoning University
文摘For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Douglas operator is characterized.
文摘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 <em>v</em>-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.
文摘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), complete results are obtained.
文摘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 v-dimensional lattice.
文摘In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter＇s and approximate essential spectrum.
文摘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,...,＋∞}.
文摘We consider the energy operator of four-electron systems in an impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensional lattice. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-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 four-electron systems in an impurity Hubbard model. The investigations show that there are such cases: 1) the essential spectrum of the system consists of the union of no more than eight segments, and the discrete spectrum of the system consists of no more than three eigenvalues;2) the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues;3) the essential spectrum of the system consists of the union of no more than three segments, and the discrete spectrum of the system is the empty set. Consequently, the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.
文摘In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of closed densely defined linear operators on Banach spaces.
基金Supported by the Natural Science Foundation of the Department of Education of Henan Province（12B110025, 102300410012）
文摘An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.
基金The author thanks S.Kotani for introducing[7]and[9]to him and R.O˘ınarov for sending him the original version of[12].Thanks are also given to H.J.Zhang and Z.W.Liao for their corrections of an earlier version of the paper.Research supported in part by the National Natural Science Foundation of China(No.11131003)the“985”project from the Ministry of Education in China,and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘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 operators.Interestingly,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 context.All of them are illustrated by examples.The 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.
文摘When A ∈ B（H） and B ∈ B（K） are given, we denote by Me the operator matrix acting on the infinite dimensional separable Hilbert space H ＋ K of the form Me = （ A C O B）. In this paper, a necessary and sufficient condition for Me to be left Fredholm for some C ∈ F（K, H） （C ∈ Inv（K, H）） is given, where F（K,H） and Inv（K, H） denote respectively, the set of Fredholm operators and the set of invertible operators of B（K, H）. In addition, we give a necessary and sufficient condition for Me to be left Fredholm for all C ∈ Inv（K, H）.
文摘This paper discusses the connectivity of the essential spectra of Toeplitz operators with symbols in H∞ +C on Hardy spaces and weighted Bergman spaces for several complex variables.
基金Foundation item： the National Natural Science Foundation of China （No. 10726043）.
文摘Let MX=（A C X B ）be a 2×2 operator matrix acting on the Hilbert space H＋K. For given A∈B（H）,B∈B（K）and C∈B（K,H）the set UX∈B（H,K）^σe（MX）is determined, whereσe（T）denotes the essential spectrum.
基金Supported by the WIMCS,Creative Research Group Fund of the National Natural Science Foundation of China (No.10721091)the 973-Project
文摘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.
文摘This paper presents the analysis of exponential stability of a system consisting of a robot and its associated safety mechanism. The system have various modes of failures and is repairable. The paper investigates the nonnegative stead-state solution of system,the existence of strictly dominant eigenvalue and restriction of essential spectrum growth bound of the system operator. The essential spectral radius of the system operator is also discussed before and after perturbation. The results show that the dynamic solution of the system is exponential stab＇flity and converges to the steady-state solution.
文摘The paper presents a model of a redundant robot configuration with a built-in safety. By the method of strong continuous semi-group, the paper analyzes the essential spectrum of the system operator before and after perturbation. The results show that in s special condition, the dynamic solution of the system is exponential stability and tends to the steady solution of the system.
