A nonself-adjoint singular Sturm-Liouville problem with a spectral parameter in the boundary condition

DOI10.1002/mana.200310269zbMath1089.34023OpenAlexW2080713286MaRDI QIDQ3022677

Bilender P. Allahverdiev

Publication date: 30 June 2005

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200310269

zbMATH Keywords

characteristic functionfunctional modelmaximal dissipative operatorselfadjoint dilationspectral parameter in the boundary conditioncompleteness of the system of eigenvectors and associated vectorsNonselfadjoint singular Sturm-Liouville problem

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Canonical models for contractions and nonselfadjoint linear operators (47A45) Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter (34B07) Linear accretive operators, dissipative operators, etc. (47B44)

Related Items (15)

A dissipative singular Sturm-Liouville problem with a spectral parameter in the boundary condition ⋮ Regular fractional dissipative boundary value problems ⋮ Spectral analysis of a nonselfadjoint Schrödinger problem with eigenparameter in the boundary condition ⋮ Dissipative Sturm-Liouville operators with transmission conditions ⋮ Direct approach for the characteristic function of a dissipative operator with distributional potentials ⋮ A nonself-adjoint 1D singular Hamiltonian system with an eigenparameter in the boundary condition ⋮ On spectral properties of dissipative fourth order boundary-value problem with a spectral parameter in the boundary condition ⋮ Dissipative operator and its Cayley transform ⋮ On the completeness of eigenfunctions of a discontinuous Dirac operator with an eigenparameter in the boundary condition ⋮ A new method for dissipative dynamic operator with transmission conditions ⋮ Spectral analysis of \(q\)-Sturm-Liouville problem with the spectral parameter in the boundary condition ⋮ Spectral analysis of eigenparameter dependent boundary value transmission problems ⋮ Completeness theorem for eigenparameter dependent dissipative Dirac operator with general transfer conditions ⋮ Unnamed Item ⋮ Minimality of eigenfunctions and associated functions of ordinary differential operators

Cites Work

• Dissipative Sturm-Liouville operators
• Limit-point and limit-circle criteria for Sturm-Liouville equations with intermittently negative principal coefficients
• Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions
• Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
• Oscillation theory for indefinite Sturm-Liouville problems with eigenparameter-dependent boundary conditions

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