Boundary systems and (skew-)self-adjoint operators on infinite metric graphs

Carsten Schubert, Christian Seifert, Jürgen Voigt, Marcus Waurick

Research output: Contribution to journalArticle

8 Citations (Scopus)

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-orthogonal 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.
Original languageEnglish
Pages (from-to)1776-1785
Number of pages10
JournalMathematische Nachrichten
Volume288
Issue number14-15
Early online date6 May 2015
DOIs
Publication statusPublished - 31 Oct 2015

Keywords

  • (skew)-self-adjoint operators
  • quantum graphs
  • boundary triple

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