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arXiv · 1308.2635

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

Carsten Schubert·Christian Seifert·Jürgen Voigt·Marcus Waurick
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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-ortho-gonal 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.

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Carsten Schubert, Christian Seifert, Jürgen Voigt, Marcus Waurick. 2013-08-12. Boundary systems and (skew-)self-adjoint operators on infinite metric graphs. https://arxiv.org/abs/1308.2635

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