Self-adjoint extensions for second-order symmetric linear difference equations

DOI10.1016/j.laa.2010.10.003zbMath1210.39004OpenAlexW2071885223MaRDI QIDQ624347

Huaqing Sun, Yuming Shi

Publication date: 9 February 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.10.003

zbMATH Keywords

Glazman-Kreĭn-Naimark theoryHermitian subspacessecond-order symmetric linear difference equationself-adjoint operator extensionself-adjoint subspace extension

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Linear symmetric and selfadjoint operators (unbounded) (47B25) Discrete version of topics in analysis (39A12) Difference operators (39A70) Linear difference equations (39A06)

Related Items (39)

Characterization of self-adjoint extensions for discrete symplectic systems ⋮ \(J\)-self-adjoint extensions for second-order linear difference equations with complex coefficients ⋮ Stability of deficiency indices for discrete Hamiltonian systems under bounded perturbations ⋮ Relatively bounded perturbations of a closed linear relation and its adjoint ⋮ The positive and negative deficiency indices of formally self-adjoint difference equations ⋮ Stability of deficiency indices of Hermitian subspaces under relatively bounded perturbations ⋮ Perturbations of spectra of closed subspaces in Banach spaces ⋮ Discrete symplectic systems, boundary triplets, and self-adjoint extensions ⋮ Spectral properties of singular discrete linear Hamiltonian systems ⋮ Spectral properties of self-adjoint subspaces ⋮ Friedrichs extensions of a class of discrete Hamiltonian systems with one singular endpoint ⋮ On discrete symplectic systems: associated maximal and minimal linear relations and nonhomogeneous problems ⋮ Limit Point Criteria for Second-Order Sturm–Liouville Equations on Time Scales ⋮ Regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint ⋮ Relationships between perturbations of a linear relation and its operator part ⋮ On the maximal subspaces of discrete Hamiltonian systems ⋮ Defect indices and definiteness conditions for a class of discrete linear Hamiltonian systems ⋮ Approximation of eigenvalues below the essential spectra of singular second-order symmetric linear difference equations ⋮ The theory for \(J\)-Hermitian subspaces in a product space ⋮ Regular approximations of spectra of singular second-order symmetric linear difference equations ⋮ Self-adjoint extensions for discrete linear Hamiltonian systems ⋮ Trace class perturbation of closed linear relations ⋮ Boundedness and closedness of linear relations ⋮ Stability of essential spectra of self-adjoint subspaces under compact perturbations ⋮ A new method for dissipative dynamic operator with transmission conditions ⋮ Deficiency indices and spectrum of fourth order difference equations with unbounded coefficients ⋮ Resolvent convergence and spectral approximations of sequences of self-adjoint subspaces ⋮ On a completely non-unitary contraction and associated dissipative difference operator ⋮ Essential spectra of self-adjoint relations under relatively compact perturbations ⋮ Regular approximations of isolated eigenvalues of singular second-order symmetric linear difference equations ⋮ Defect index of the square of a formally self-adjoint second-order difference expression ⋮ \(\mathcal{J}\)-self-adjoint extensions of a class of Hamiltonian differential systems ⋮ On the stability of self-adjointness of linear relations ⋮ Linear operators associated with differential and difference systems: what is different? ⋮ Invariance of deficiency indices of second-order symmetric linear difference equations under perturbations ⋮ \(J\)-self-adjoint extensions for a class of discrete linear Hamiltonian systems ⋮ Sturm-Liouville problem via coulomb type in difference equations ⋮ On the density of the minimal subspaces generated by discrete linear Hamiltonian systems ⋮ Absolutely continuous spectrum of fourth order difference equations

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