# Symbolic Calculus for a Class of Pseudodifferential Operators with Applications to Compactness

## TL;DR

This paper develops a symbolic calculus for pseudodifferential operators and applies it to study compactness in L2 spaces.

## Contribution

The paper introduces a symbolic calculus for pseudodifferential operators and applies it to compactness in L2.

## Key findings

- A symbolic calculus is established for a class of pseudodifferential operators.
- The calculus is applied to prove compactness results in L2 spaces using a compact version of the T(1) theorem.

## Abstract

We prove a symbolic calculus for a class of pseudodifferential operators, and discuss its applications to \documentclass[12pt]{minimal}
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\begin{document}$$L^2$$\end{document}L2-compactness via a compact version of the T(1) theorem.