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

Publikationstyp
Journal Article
Date Issued
2015-04-15
Sprache
English
Author(s)
Schubert, Carsten  
Seifert, Christian  orcid-logo
Voigt, Jürgen  
Waurick, Marcus  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/10805
Journal
Mathematische Nachrichten  
Volume
288
Issue
14/15
Start Page
1776
End Page
1785
Citation
Mathematische Nachrichten 288 (14/15): 1776-1785 (2015-10-01)
Publisher DOI
10.1002/mana.201500054
Scopus ID
2-s2.0-84946173736
Publisher
Wiley-VCH
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.
Subjects
(skew-)self-adjoint operators
05C99
35Q99
47B25
Boundary triple
Quantum graphs
DDC Class
510: Mathematik