A class of $n$-entire Schr\"odinger operators

TL;DR

This paper classifies certain singular Schr"odinger operators as $n$-entire, providing spectral characterizations for radial cases using de Branges space methods, advancing understanding of their selfadjoint extensions.

Contribution

It introduces conditions for symmetric operators to be in the $n$-entire class and applies this to spectral analysis of radial Schr"odinger operators.

Findings

Characterization of $n$-entire Schr"odinger operators.

Spectral description of radial Schr"odinger operators.

Use of de Branges space techniques for analysis.

Abstract

We study singular Schr\"odinger operators on a finite interval as selfadjoint extensions of a symmetric operator. We give sufficient conditions for the symmetric operator to be in the $n$-entire class, which was defined in our previous work, for some $n$. As a consequence of this classification, we obtain a detailed spectral characterization for a wide class of radial Schr\"odinger operators. The results given here make use of de Branges Hilbert space techniques.