Pavel Kurasov: MAXIMAL DISSIPATIVE OPERATORS ON METRIC GRAPHS

Abstract.

Dissipative Schrödinger operators on metric graphs are discussed. Vertex conditions leading to maximal dissipative operators are characterised. The language of hypergraphs is used to determine possible spectral multiplicity 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 characterisation of all completely non-self-adjoint operators.