Non-self-adjoint graphs

Amru Hussein*, David Krejčiřík, Petr Siegl

*Corresponding author for this work

Research output: Contribution to journalArticle

11 Citations (Scopus)
6 Downloads (Pure)

Abstract

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

Original languageEnglish
Pages (from-to)2921-2957
Number of pages37
JournalTransactions of the American Mathematical Society
Volume367
Issue number4
Early online date13 Aug 2014
DOIs
Publication statusPublished - Apr 2015
Externally publishedYes

Keywords

  • Laplacians on metric graphs
  • Non-self-adjoint boundary conditions
  • Riesz basis
  • Similarity transforms to self-adjoint operators

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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