The spectra of selfadjoint extensions of entire operators with deficiency indices (1,1)

TL;DR

This paper characterizes the spectra of selfadjoint extensions of entire operators with deficiency indices (1,1) using de Branges space techniques, extending previous results to non-dense domains.

Contribution

It provides necessary and sufficient conditions for spectra of such operators, generalizing earlier work to include non-dense domain cases.

Findings

Spectral characterization using de Branges spaces.

Extension of Krein's functional model.

Applicable to non-dense domain operators.

Abstract

We give necessary and sufficient conditions for real sequences to be the spectra of selfadjoint extensions of an entire operator whose domain may be non-dense. For this spectral characterization we use de Branges space techniques and a generalization of Krein's functional model for simple, regular, closed, symmetric operators with deficiency indices (1,1). This is an extension of our previous work in which similar results were obtained for densely defined operators.