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 language | English |
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Pages (from-to) | 2921-2957 |
Number of pages | 37 |
Journal | Transactions of the American Mathematical Society |
Volume | 367 |
Issue number | 4 |
Early online date | 13 Aug 2014 |
DOIs | |
Publication status | Published - Apr 2015 |
Externally published | Yes |
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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Petr Siegl
- School of Mathematics and Physics - Visiting Scholar
- Mathematical Sciences Research Centre
Person: Academic