The defect index of singular symmetric linear difference equations with real coefficients

DOI10.1090/S0002-9939-10-10253-6zbMath1196.39003MaRDI QIDQ3574821

Guojing Ren, Yuming Shi

Publication date: 2 July 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

asymptotic behaviorslimit point casedefect indexsquare summable solutionsingular symmetric linear difference equationstrong limit point case

Mathematics Subject Classification ID

Weyl theory and its generalizations for ordinary differential equations (34B20) Additive difference equations (39A10) Discrete version of topics in analysis (39A12)

Related Items (18)

Stability of deficiency indices for discrete Hamiltonian systems under bounded perturbations ⋮ The positive and negative deficiency indices of formally self-adjoint difference equations ⋮ Stability of deficiency indices of Hermitian subspaces under relatively bounded perturbations ⋮ Deficiency indices of the polynomials of formally self-adjoint difference expressions ⋮ Spectral properties of singular discrete linear Hamiltonian systems ⋮ On discrete symplectic systems: associated maximal and minimal linear relations and nonhomogeneous problems ⋮ Functional model and spectral analysis of discrete singular Hamiltonian system ⋮ Defect indices and definiteness conditions for a class of discrete linear Hamiltonian systems ⋮ Defect indices of singular symmetric linear difference equations with complex coefficients ⋮ Error estimate of eigenvalues of perturbed higher-order discrete vector boundary value problems ⋮ Deficiency indices and spectrum of fourth order difference equations with unbounded coefficients ⋮ Weyl-Titchmarsh theory for time scale symplectic systems on half line ⋮ Defect index of the square of a formally self-adjoint second-order difference expression ⋮ Invariance of deficiency indices of second-order symmetric linear difference equations under perturbations ⋮ Invariance of deficiency indices under perturbation for discrete Hamiltonian systems ⋮ Extensions and spectral problems of 1D discrete Hamiltonian systems ⋮ Spectral theory of higher order difference operators ⋮ Absolutely continuous spectrum of fourth order difference equations

Cites Work

• Unnamed Item
• Unnamed Item
• On Weyl-Titchmarsh theory for singular finite difference Hamiltonian systems
• Spectral analysis of second order difference equations
• The limit circle and limit point criteria for second-order linear difference equations
• A spectral analysis for self-adjoint operators generated by a class of second order difference equations
• Limit-point and limit-circle criteria for singular second-order linear difference equations with complex coefficients
• Weyl--Titchmarsh theory for a class of discrete linear Hamiltonian systems
• Discrete and continuous boundary problems
• Strong limit point criteria for a class of singular discrete linear Hamiltonian systems
• Second-order Sturm-Liouville difference equations and orthogonal polynomials
• The deficiency index problem for ordinary selfadjoint differential operators
• Extension theory of formally normal and symmetric subspaces
• Asymptotic Behavior of Solutions of Ordinary Difference Equations

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