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arXiv · 1308.4264

Non-self-adjoint graphs

Amru Hussein·David Krejcirik·Petr Siegl
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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 how to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

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BibTeXRIS

Amru Hussein, David Krejcirik, Petr Siegl. 2013-08-20. Non-self-adjoint graphs. https://doi.org/10.1090/s0002-9947-2014-06432-5

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