Nuclear pseudo-differential operators in Besov spaces on compact Lie groups

TL;DR

This paper investigates the properties of nuclear pseudo-differential operators on Besov spaces over compact Lie groups, establishing key approximation and trace formulas for operators with limited symbol regularity.

Contribution

It establishes the metric approximation property for Besov spaces on compact Lie groups and derives trace formulas for nuclear Fourier multipliers and pseudo-differential operators.

Findings

Proved the metric approximation property for Besov spaces on compact Lie groups.

Derived trace formulas for nuclear Fourier multipliers.

Analyzed r-nuclearity and trace properties of pseudo-differential operators with limited regularity.

Abstract

In this work we establish the metric approximation property for Besov spaces defined on arbitrary compact Lie groups. As a consequence of this fact, we investigate trace formulae for nuclear Fourier multipliers on Besov spaces. Finally, we study the r-nuclearity, the Grothendieck-Lidskii formula and the (nuclear) trace of pseudo-differential operators in generalized H\"ormander classes acting on periodic Besov spaces. We will restrict our attention to pseudo-differential operators with symbols of limited regularity.