A completeness theorem for a dissipative Schrödinger problem with the spectral parameter in the boundary condition

DOI10.1002/mana.200410623zbMath1145.34054OpenAlexW1968718268MaRDI QIDQ5385218

Mevlüde Yakıt Ongun, Bilender P. Allahverdiev

Publication date: 5 May 2008

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

Full work available at URL: https://doi.org/10.1002/mana.200410623

zbMATH Keywords

completenessself-adjoint dilationmaximal dissipative operatorLax-Phillips scatteringspectral parameter in boundary conditionnon-selfadjoint singular Schrödinger operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Dilations, extensions, compressions of linear operators (47A20) Linear boundary value problems for ordinary differential equations (34B05) Canonical models for contractions and nonselfadjoint linear operators (47A45) Scattering theory of linear operators (47A40) Linear accretive operators, dissipative operators, etc. (47B44) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

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Cites Work

• Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions
• Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
• Spectral analysis of dissipative Schrödinger operators
• Unnamed Item