Symbolic calculus for a class of pseudodifferential operators with applications to compactness

TL;DR

This paper develops a symbolic calculus for a specific class of pseudodifferential operators and applies it to establish criteria for their compactness on L^2 spaces.

Contribution

It introduces a new symbolic calculus framework and demonstrates its use in analyzing the compactness of pseudodifferential operators.

Findings

Established a symbolic calculus for the class of operators.

Provided criteria for L^2-compactness using a compact T(1) theorem.

Enhanced understanding of operator compactness in pseudodifferential analysis.

Abstract

We prove a symbolic calculus for a class of pseudodifferential operators, and discuss its applications to $L^2$-compactness via a compact version of the $T(1)$ theorem.