Spectral analysis of \(q\)-Sturm-Liouville problem with the spectral parameter in the boundary condition
type: Item
instance of: scholarly article
title: Spectral analysis of \(q\)-Sturm-Liouville problem with the spectral parameter in the boundary condition
zbMATH Open document ID: 1273.39010
DOI: 10.1155/2012/736437
author: Aytekin Eryılmaz
published in: Journal of Function Spaces and Applications
publication date: 2012-11-07T00:00:00Z
review text: Many studies have been conducted regarding the spectral analysis of the Sturm-Liouville and Schrödinger differential equations, as well as discrete equations, with the spectral parameter in the boundary conditions. With the recent interest in quantum calculus, a number of investigators analyzed many aspects of the \(q\)-difference equations, including properties of eigenvalues and eigenvectors. In the current work, the author investigates the \(q\)-Sturm-Liouville boundary value problem in an appropriate Hilbert space, with an emphasis on the dissipation at the right endpoint and with the spectral parameter at zero. The functional model of the dissipative operator is constructed, and the theorems of completeness of the system of eigenvalues and corresponding eigenvectors of the dissipative \(q\)-difference operator, are presented.
reviewed by: Shlomo Carmi
Mathematics Subject Classification ID: 39A13
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 6102740
zbMATH Keywords: \(q\)-Sturm-Liouville boundary value problem
zbMATH Keywords: Hilbert space
zbMATH Keywords: spectral parameters
zbMATH Keywords: eigenvalues
zbMATH Keywords: eigenvectors
zbMATH Keywords: \(q\)-difference equations
Wikidata QID: Q58908384
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/736437
OpenAlex ID: W2077123642
cites work: ON THE SPECTRAL THEORY OF DISSIPATIVE DIFFERENCE OPERATORS OF SECOND ORDER
cites work: Dissipative Second-Order Difference Operators with General Boundary Conditions
cites work: A nonself-adjoint singular Sturm-Liouville problem with a spectral parameter in the boundary condition
cites work: Extensions, Dilations and Functional Models of Infinite Jacobi Matrix
cites work: A dissipative singular Sturm-Liouville problem with a spectral parameter in the boundary condition
cites work: Discrete and continuous boundary problems
cites work: Scattering theory for open quantum systems with finite rank coupling
cites work: Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
cites work: Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions
cites work: Q5571194
cites work: Q4004417
cites work: An eigenvalue problem for quadratic pencils of \(q\)-difference equations and its applications
cites work: A completeness theorem for a dissipative Schrödinger problem with the spectral parameter in the boundary condition
cites work: SELFADJOINT DILATION OF THE DISSIPATIVE SCHRÖDINGER OPERATOR AND ITS RESOLUTION IN TERMS OF EIGENFUNCTIONS
cites work: ICIAM/GAMM 95 Applied sciences, especially Mechanics Minisymposia Contributions
cites work: Non-selfadjoint difference operators and Jacobi matrices with spectral singularities
cites work: A spectral analysis for self-adjoint operators generated by a class of second order difference equations
cites work: Boundary conditions at infinity for difference equations of limit-circle type
cites work: Quantum calculus
cites work: Spectral analysis of \(q\)-difference equations with spectral singularities
cites work: Q4942162
cites work: Spectral theory of Sturm-Liouville difference operators
cites work: Basic Sturm–Liouville problems
cites work: Q4862628
cites work: Q5539945
cites work: Q5579836
description: scientific article; zbMATH DE number 6102740