Localization principle for compact Hankel operators

TL;DR

This paper establishes a localization principle for compact Hankel operators, showing that disjoint parts of the symbol's singular support independently influence the asymptotic behavior of singular values, with explicit formulas derived.

Contribution

It introduces a localization principle for Hankel operators, enabling explicit asymptotic analysis based on symbol behavior near singular support.

Findings

Disjoint parts of the symbol's singular support contribute independently to singular value asymptotics.

Explicit formulas for the leading term of singular value asymptotics are derived.

The principle applies to both Hankel integral operators and infinite matrices.

Abstract

In the power scale, the asymptotic behavior of the singular values of a compact Hankel operator is determined by the behavior of the symbol in a neighborhood of its singular support. In this paper, we discuss the localization principle which says that the contributions of disjoint parts of the singular support of the symbol to the asymptotic behavior of the singular values are independent of each other. We apply this principle to Hankel integral operators and to infinite Hankel matrices. In both cases, we describe a wide class of Hankel operators with power-like asymptotics of singular values. The leading term of this asymptotics is found explicitly.