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.
- Laplacians on metric graphs
- Non-self-adjoint boundary conditions
- Riesz basis
- Similarity transforms to self-adjoint operators
ASJC Scopus subject areas
- Applied Mathematics