TY - JOUR

T1 - MAXIMAL DISSIPATIVE OPERATORS ON METRIC GRAPHS: REAL EIGENVALUES AND THEIR MULTIPLICITIES

AU - Kurasov, P.

AU - Muller, J.

AU - Naboko, S.

N1 - Export Date: 05 February 2026; Cited By: 0

PY - 2025

Y1 - 2025

N2 - 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. © 2025 by the author(s).

AB - 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. © 2025 by the author(s).

U2 - 10.1090/btran/218

DO - 10.1090/btran/218

M3 - статья

VL - 12

SP - 576

EP - 629

JO - Transactions of the American Mathematical Society Series B

JF - Transactions of the American Mathematical Society Series B

SN - 2330-0000

ER -