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 |
|---|---|
| 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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Cite this
Hussein, A., Krejčiřík, D., & Siegl, P. (2015). Non-self-adjoint graphs. Transactions of the American Mathematical Society, 367(4), 2921-2957. https://doi.org/10.1090/S0002-9947-2014-06432-5