Unbounded Hankel operators and moment problems

TL;DR

This paper establishes simple criteria for the closability of non-negative Hankel quadratic forms and defines unbounded Hankel operators under minimal assumptions, extending classical boundedness conditions.

Contribution

It provides necessary and sufficient conditions for the closability of Hankel quadratic forms and describes the domain of the associated unbounded Hankel operators.

Findings

Criteria for closability of Hankel forms

Description of the domain of unbounded Hankel operators

Extension of classical boundedness conditions

Abstract

We find simple conditions for a non-negative Hankel quadratic form to be closable. Under some mild a priori assumption on the associated moments these sufficient conditions turn out to be also necessary. We also describe the domain of the corresponding closed form. This allows us to define unbounded non-negative Hankel operators under minimal assumptions on their matrix elements. The results obtained supplement the classical Widom condition for a Hankel operator to be bounded..