This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem...This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.展开更多
An operator T on a complex separable infinite dimensional Hilbert space is hypercyclic if there is a vector y∈H such that the orbit Orb(T,y)={y,Ty,T^(2)y,T^(3)y,...}is dense in H.Hypercyclic property and supercyclic ...An operator T on a complex separable infinite dimensional Hilbert space is hypercyclic if there is a vector y∈H such that the orbit Orb(T,y)={y,Ty,T^(2)y,T^(3)y,...}is dense in H.Hypercyclic property and supercyclic proeprty are liable to fail for 2×2 upper triangular operator matrices.In this paper,we aim to explore and characterize the hypercyclicity and the supercyclicity for 2×2 upper triangular operator matrices.We obtain a spectral characterization of the norm-closure of the class of all hypercyclic(supercyclic)operators for 2×2 upper triangular operator matrices.展开更多
Given two closed, in general unbounded, operators A and C, we investigate the left invertible completion of the partial operator matrix A ？ 0 C. Based on the space decomposition technique, the alternative sufficient ...Given two closed, in general unbounded, operators A and C, we investigate the left invertible completion of the partial operator matrix A ？ 0 C. Based on the space decomposition technique, the alternative sufficient and necessary conditions are given according to whether the dimension of R（A）⊥ is finite or infinite.As a direct consequence, the perturbation of left spectra is further presented.展开更多
Property(R)holds for an operator when the complement in the approximate point spectrum of the Browder essential approximate point spectrum coincides with the isolated points of the spectrum which are eigenvalues of fi...Property(R)holds for an operator when the complement in the approximate point spectrum of the Browder essential approximate point spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity.Let A∈B(H)and B∈B(K),where H and K are complex infinite dimensional separable Hilbert spaces.We denote by M_(C)the operator acting on H⊕K of the form M_(C)=(AC0B).In this paper,we give a sufficient and necessary condition for M_(C)∈(R)for all C∈B(K,H).展开更多
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)the National Natural Science Foundation of China (No. 10962004)
文摘This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.
基金Supported by National Natural Science Foundation of China(Grant No.11671201)。
文摘An operator T on a complex separable infinite dimensional Hilbert space is hypercyclic if there is a vector y∈H such that the orbit Orb(T,y)={y,Ty,T^(2)y,T^(3)y,...}is dense in H.Hypercyclic property and supercyclic proeprty are liable to fail for 2×2 upper triangular operator matrices.In this paper,we aim to explore and characterize the hypercyclicity and the supercyclicity for 2×2 upper triangular operator matrices.We obtain a spectral characterization of the norm-closure of the class of all hypercyclic(supercyclic)operators for 2×2 upper triangular operator matrices.
基金partially supported by the Natural Science Foundation of China(Nos.11461049 and 11371185)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20111501110001)+3 种基金the ‘Chunhui Program’ of the Ministry of Education of China(No.Z2009-1-01010)the Major Program of the National Natural Science Foundation of Inner Mongolia(No.2013ZD01)the National Science Foundation for Fostering Distinguished Young Scholars of Inner Mongolia(No.2013JQ01)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia(No.NJYT-12-B06)
文摘Given two closed, in general unbounded, operators A and C, we investigate the left invertible completion of the partial operator matrix A ？ 0 C. Based on the space decomposition technique, the alternative sufficient and necessary conditions are given according to whether the dimension of R（A）⊥ is finite or infinite.As a direct consequence, the perturbation of left spectra is further presented.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.GK 202007002)Nature Science Basic Research Plan in Shaanxi Province of China(Grant No.2021JM-189,2021JM-519)。
文摘Property(R)holds for an operator when the complement in the approximate point spectrum of the Browder essential approximate point spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity.Let A∈B(H)and B∈B(K),where H and K are complex infinite dimensional separable Hilbert spaces.We denote by M_(C)the operator acting on H⊕K of the form M_(C)=(AC0B).In this paper,we give a sufficient and necessary condition for M_(C)∈(R)for all C∈B(K,H).
