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

Carsten Schubert, Christian Seifert, Jürgen Voigt, Marcus Waurick

Research output: Contribution to journalArticle

7 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

Fingerprint

Metric Graphs
Infinite Graphs
Self-adjoint Operator
Skew
Subspace
Symmetric Operator
Unitary Operator
Laplace
Boundary Value
Orthogonality
Derivative
Generalise
Graph in graph theory
Operator

Keywords

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

Cite this

Schubert, Carsten ; Seifert, Christian ; Voigt, Jürgen ; Waurick, Marcus. / Boundary systems and (skew-)self-adjoint operators on infinite metric graphs. In: Mathematische Nachrichten. 2015 ; Vol. 288, No. 14-15. pp. 1776-1785.
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Boundary systems and (skew-)self-adjoint operators on infinite metric graphs. / Schubert, Carsten; Seifert, Christian; Voigt, Jürgen; Waurick, Marcus.

In: Mathematische Nachrichten, Vol. 288, No. 14-15, 31.10.2015, p. 1776-1785.

Research output: Contribution to journalArticle

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