Riesz basis property of generalized eigenfunctions for many interval eigenvalue problems with eigenparameter dependent boundary-transmission conditions

The main goal of this study is to provide an operator-pencil framework for the investigation of many-interval boundary-value-transmission problems (BVTP) with eigenparameter appearing in the boundary-transmission conditions. By applying an our own approaches the considered problem is transformed int...

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Bibliographic Details
Main Author: Olğar, Hayati
Format: Conference Proceeding
Language:English
Subjects:
Boundary value problems
Eigenvalues
Eigenvectors
Hilbert space
Integral equations
Operators (mathematics)
Sobolev space
Online Access:Get full text
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Summary:The main goal of this study is to provide an operator-pencil framework for the investigation of many-interval boundary-value-transmission problems (BVTP) with eigenparameter appearing in the boundary-transmission conditions. By applying an our own approaches the considered problem is transformed into an eigenvalue problem for suitable integral equation in terms of which it is defined a concept of generalized eigenfunctions. We introduce some self-adjoint compact operators in suitable Sobolev spaces such a way that the considered problem can be reduced to an operator-pencil equation. Finally, it is shown that the spectrum is discrete and the set of generalized eigenfunctions form a Riesz basis of the suitable Hilbert space.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5049068