Boundary systems and (skew-)self-adjoint operators on infinite metric graphs
Functional Analysis
2016-06-28 v1
Abstract
We generalize the notion of Lagrangian subspaces to self-orthogonal subspaces with respect to a (skew-)symmetric form, thus characterizing (skew-)self-adjoint and unitary operators by means of self-ortho-gonal subspaces. By orthogonality preserving mappings, these characterizations can be transferred to abstract boundary value spaces of (skew-)symmetric operators. Introducing the notion of boundary systems we then present a unified treatment of different versions of boundary triples and related concepts treated in the literature. The application of the abstract results yields a description of all (skew-)self-adjoint realizations of Laplace and first derivative operators on graphs.
Keywords
Cite
@article{arxiv.1308.2635,
title = {Boundary systems and (skew-)self-adjoint operators on infinite metric graphs},
author = {Carsten Schubert and Christian Seifert and Jürgen Voigt and Marcus Waurick},
journal= {arXiv preprint arXiv:1308.2635},
year = {2016}
}