Inverse spectral theory for a class of non-compact Hankel operators

TL;DR

This paper develops an inverse spectral theory for a specific class of non-compact Hankel operators, characterizing their spectral data and identifying conditions for boundedness and finite spectrum of their squared operators.

Contribution

It provides a complete characterization of spectral data for bounded Hankel operators with finite spectrum of their squared operators, advancing inverse spectral theory in this area.

Findings

Characterization of all bounded Hankel operators with finite spectrum of $\Gamma^*\Gamma$

Identification of spectral data corresponding to these operators

Construction of inverse spectral theory for this class

Abstract

We characterize all bounded Hankel operators $\Gamma $ such that $\Gamma^*\Gamma$ has finite spectrum. We identify spectral data corresponding to such operators and construct inverse spectral theory including the characterization of these spectral data.