Non-self-adjoint graphs

Hussein, Amru; Krejčiřík, David; Siegl, Petr

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

Non-self-adjoint graphs
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by Amru Hussein, David Krejčiřík and Petr Siegl PDF

Trans. Amer. Math. Soc. 367 (2015), 2921-2957 Request permission

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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