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Non-self-adjoint graphs


Authors: Amru Hussein, David Krejčiřík and Petr Siegl
Journal: Trans. Amer. Math. Soc. 367 (2015), 2921-2957
MSC (2010): Primary 34B45, 47A10, 81Q12; Secondary 47B44
DOI: https://doi.org/10.1090/S0002-9947-2014-06432-5
Published electronically: August 13, 2014
MathSciNet review: 3301887
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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.


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Additional Information

Amru Hussein
Affiliation: Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, 55099 Mainz, Germany
Email: hussein@mathematik.uni-mainz.de

David Krejčiřík
Affiliation: Department of Theoretical Physics, Nuclear Physics Institute ASCR, 25068 Řež, Czech Republic
Email: krejcirik@ujf.cas.cz

Petr Siegl
Affiliation: Mathematical Institute, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
Email: petr.siegl@math.unibe.ch

DOI: https://doi.org/10.1090/S0002-9947-2014-06432-5
Keywords: Laplacians on metric graphs, non-self-adjoint boundary conditions, similarity transforms to self-adjoint operators, Riesz basis
Received by editor(s): June 24, 2013
Published electronically: August 13, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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