Non-self-adjoint graphs
Spectral Theory
2021-03-30 v1 Mathematical Physics
math.MP
Quantum Physics
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.
Cite
@article{arxiv.1308.4264,
title = {Non-self-adjoint graphs},
author = {Amru Hussein and David Krejcirik and Petr Siegl},
journal= {arXiv preprint arXiv:1308.4264},
year = {2021}
}
Comments
43 pages, 1 figure