Point spectrum of the schrödinger operator with point interactions at the vertices of regular <em class="a-plus-plus">N</em>-gons

Abstract

We present a complete description of the point spectrum of the Laplace operator perturbed by point potentials concentrated at the vertices of regular polygons. We prove a criterion for the absence of points of the point spectrum of a singular perturbed positive self-adjoint operator with the property of cyclicity of defect vectors.