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

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.