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. |
URI: | http://hdl.handle.net/11420/10805 | ISSN: | 1522-2616 | Journal: | Mathematische Nachrichten | Institute: | Mathematik E-10 | Document Type: | Article |
Appears in Collections: | Publications without fulltext |
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