Pavel Kurasov: M-functions and maximal dissipative operators on metric graphs

Date: 2024-06-14

Time: 09:50 - 10:40

Pavel Kurasov, University of Stockholm

M-functions are proven be a standard tool in spectral theory of one-dimensional Schr\”odinger operators. Their generalisations for metric graphs not only allow one to describe spectra of graphs but serve as ideal set of spectral data to solve inverse problems. M-functions can be used to produce families of isospectral graphs. In the current talk we shall discuss how this language can be applied to analyse dissipative Schroedinger operators on metric graphs. The language of hypergraphs is introduced and 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 operators not possessing any self-adjoint reduction, so-called completely non-self-adjoint operators, on compact metric graphs with delta couplings at the vertices.