Spectral transition model with the general contact interaction

Abstract

Using a technique introduced by Sergei Naboko, we analyze a generalization of the parameter-controlled model of spectral transition, originally proposed by Smilansky and Solomyak, to the situation where the singular interaction responsible for the effect is characterized by the `full' family of four real numbers with the `diagonal' part of the coupling being position-dependent.

24 pages, to appear in "From Complex Analysis to Operator Theory: A Panorama In Memory of Sergey Naboko"