Publisher DOI: 10.1002/mana.201500054
Title: Boundary systems and (skew-)self-adjoint operators on infinite metric graphs
Language: English
Authors: Schubert, Carsten 
Seifert, Christian  
Voigt, Jürgen 
Waurick, Marcus 
Keywords: (skew-)self-adjoint operators; 05C99; 35Q99; 47B25; Boundary triple; Quantum graphs
Issue Date: 15-Apr-2015
Publisher: Wiley-VCH
Source: Mathematische Nachrichten 288 (14/15): 1776-1785 (2015-10-01)
Abstract (english): 
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.
ISSN: 1522-2616
Journal: Mathematische Nachrichten 
Institute: Mathematik E-10 
Document Type: Article
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