Schrodinger and polyharmonic operators on infinite graphs: Parabolic well-posedness and p-independence of spectra

We analyze properties of semigroups generated by Schriidinger operators Delta - V or polyharmonic operators -(-Delta)(m), on metric graphs both on LP-spaces and spaces of continuous functions. In the case of spatially constant potentials, we provide a semi-explicit formula for their kernel. Under an additional sub-exponential growth condition on the graph, we prove analyticity, ultracontractivity, and pointwise kernel estimates for these semigroups; we also show that their generators' spectra coincide on all relevant function spaces and present a Krein-type dimension reduction, showing that their spectral values are determined by the spectra of generalized discrete Laplacians acting on various spaces of functions supported on combinatorial graphs. (C) 2020 Published by Elsevier Inc.