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The weak eigenfunctions of boundary-value problem with symmetric discontinuities

The weak eigenfunctions of boundary-value problem with symmetric discontinuities AbstractThe main goal of thisstudy is the investigation of discontinuous boundary-value problemsfor second-order differential operators with symmetric transmissionconditions. We introduce the new notion of weak functions for suchtype of discontinuous boundary-value problems and develop anoperator-theoretic method for the investigation of the spectrum andcompleteness property of the weak eigenfunction systems.In particular, we define some self-adjoint compact operators insuitable Sobolev spaces such that the considered problem can bereduced to an operator-pencil equation. The main result of thispaper is that the spectrum is discrete and the set of eigenfunctionsforms a Riesz basis of the suitable Hilbert space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Analysis de Gruyter

The weak eigenfunctions of boundary-value problem with symmetric discontinuities

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References (9)

Publisher
de Gruyter
Copyright
© 2022 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6082
eISSN
1869-6082
DOI
10.1515/jaa-2021-2079
Publisher site
See Article on Publisher Site

Abstract

AbstractThe main goal of thisstudy is the investigation of discontinuous boundary-value problemsfor second-order differential operators with symmetric transmissionconditions. We introduce the new notion of weak functions for suchtype of discontinuous boundary-value problems and develop anoperator-theoretic method for the investigation of the spectrum andcompleteness property of the weak eigenfunction systems.In particular, we define some self-adjoint compact operators insuitable Sobolev spaces such that the considered problem can bereduced to an operator-pencil equation. The main result of thispaper is that the spectrum is discrete and the set of eigenfunctionsforms a Riesz basis of the suitable Hilbert space.

Journal

Journal of Applied Analysisde Gruyter

Published: Dec 1, 2022

Keywords: Boundary value problems; transmission conditions; weak eigenfunctions; eigenvalue; completeness; Riesz basis; 34L10; 34L15 34B08; 34B24

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