Restriction theorems for Hankel operators

TL;DR

This paper investigates the properties of restriction maps from integral Hankel operators to matrices, focusing on their boundedness in various operator norms, including the Schatten norms.

Contribution

It introduces and analyzes the boundedness of restriction maps for Hankel operators, extending understanding of their behavior in different normed settings.

Findings

Restriction maps are bounded in operator norm under certain conditions.

Averaging kernels can be used to define generalized restriction maps.

Results include criteria for boundedness in Schatten norms.

Abstract

We consider a class of maps from integral Hankel operators to Hankel matrices, which we call restriction maps. In the simplest case, such a map is simply a restriction of the integral kernel onto integers. More generally, it is given by an averaging of the kernel with a sufficiently regular weight function. We study the boundedness of restriction maps with respect to the operator norm and the Schatten norms.