Generic asymptotics of resonance counting function for Schrödinger point interactions

Abstract

We study the leading coefficient in the asymptotical formula $N(R)=\frac{W}{\pi }R+O(1)$, $R\to \infty$, for the resonance counting function $N(R)$ of Schrödinger Hamiltonians with point interactions. For such Hamiltonians, the Weyl-type and non-Weyl-type asymptotics of $N(R)$ was introduced recently in a paper by J. Lipovský and V. Lotoreichik (2017). In this note, we prove that the Weyl-type asymptotics is generic.

14 pages; the exposition of the proof of Theorem 3.2 is improved, misprints are corrected