Non-self-adjoint graphs

Amru Hussein; David Krejčiřík; Petr Siegl

doi:10.1090/S0002-9947-2014-06432-5

Non-self-adjoint graphs

Amru Hussein^*, David Krejčiřík, Petr Siegl

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

23 Downloads (Pure)

Abstract

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

Original language	English
Pages (from-to)	2921-2957
Number of pages	37
Journal	Transactions of the American Mathematical Society
Volume	367
Issue number	4
Early online date	13 Aug 2014
DOIs	https://doi.org/10.1090/S0002-9947-2014-06432-5
Publication status	Published - Apr 2015
Externally published	Yes

Keywords

Laplacians on metric graphs
Non-self-adjoint boundary conditions
Riesz basis
Similarity transforms to self-adjoint operators

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-2014-06432-5Licence: Unspecified

Non-Self-Adjoint Graphs
© 2014 American Mathematical Society. This work is made available online in accordance with the publisher’s policies. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 425 KBLicence: Unspecified

Cite this

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AU - Siegl, Petr

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AB - On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

KW - Laplacians on metric graphs

KW - Non-self-adjoint boundary conditions

KW - Riesz basis

KW - Similarity transforms to self-adjoint operators

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Non-self-adjoint graphs

Abstract

Keywords

ASJC Scopus subject areas

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