Natalia Saburova | Spectral invariants for Schrödinger operators on periodic discrete graphs

Days on Diffraction 2024. Mini-symposium “Inverse Problems”. Monday, 10 June, 2024
Natalia Yu. Saburova (Northern (Arctic) Federal Universit)
Spectral invariants for Schrödinger operators on periodic discrete graphs
We consider Schrodinger operators with real periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We construct a complete system of the Floquet spectral invariants. These spectral invariants are polynomials with respect to the potential and are obtained as coefficients of the Fourier series for the traces of the fiber Schr¨odinger operators on quotient graphs. We apply these invariants to determine isospectral potentials for some periodic graphs