Resonances on regular tree graphs

Abstract

We investigate the distribution of the resonances near spectral thresholds of Laplace operators on regular tree graphs with $k$-fold branching, $k\ge 1$, perturbed by nonself-adjoint exponentially decaying potentials. We establish results on the absence of resonances which in particular involve absence of discrete spectrum near some sectors of the essential spectrum of the operators.

References in corpus (1)

• Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees