On the nuclear trace of Fourier integral operators in $L^p$-spaces

TL;DR

This paper characterizes when Fourier integral operators are nuclear on various spaces and explores their nuclear trace, advancing understanding of their functional analysis properties.

Contribution

It provides new characterizations of nuclearity and analyzes the nuclear trace of Fourier integral operators across multiple mathematical structures.

Findings

Nuclearity criteria for Fourier integral operators on different spaces

Explicit formulas for the nuclear trace of these operators

Extension of nuclearity concepts to compact Lie groups and manifolds

Abstract

In this paper we provide characterizations for the nuclearity of Fourier integral operators on $\mathbb{R}^n,$ on the discrete group $\mathbb{Z}^n,$ arbitrary compact Lie groups and compact homogeneous manifolds. We also investigate the nuclear trace of these operators.