Work

Maximal dissipative operators on metric graphs: Real eigenvalues and their multiplicities

Year: 2025

Type: article

Abstract: Dissipative Schrödinger operators on metric graphs are discussed. Vertex conditions leading to maximal dissipative operators are characterised. The language of hypergraphs is introduced and used to determine possible spectral multiplicities of the self-adjoint reductions, which depends not only on the properties of the potential but on the topologic and geometric properties of the metric graph. This leads to the characterisation of all operators, not possessing any self-adjoint reduction, so-called completely non-self-adjoint operators, on compact metric graphs with delta couplings at the vertices.

Source: Transactions of the American Mathematical Society Series B

DOI: 10.1090/btran/218

Authors: Pavel Kurasov, Jacob Muller, Sergei Naboko

Institutions: Stockholm University, St Petersburg University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,750

Funder: Vetenskapsrådet