Boundary systems and (skew‐)self‐adjoint operators on infinite metric graphs. Issue 14 (6th May 2015)

• Record Type: Journal Article
• Authors: Schubert, Carsten; Seifert, Christian; Voigt, Jürgen; Waurick, Marcus
• Is Part Of: Mathematische Nachrichten. Volume 288:Issue 14/15(2015)
• Page Start: 1776
• Page End: 1785
• Publication Date: 2015-05-06
• Subjects: Boundary triple -- (skew‐)self‐adjoint operators -- quantum graphs -- 47B25 -- 05C99 -- 35Q99; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201500054
• Languages: English
• ISSNs: 0025-584X

Abstract

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.