# Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions

## TL;DR

This paper develops a comprehensive theory of global pseudodifferential operators of infinite order within ultradifferentiable function classes, extending previous frameworks and providing symbolic calculus and examples.

## Contribution

It introduces a new framework for infinite order pseudodifferential operators in ultradifferentiable classes, expanding the mathematical tools available for analysis.

## Key findings

- Established composition and transpose properties for these operators
- Developed symbolic calculus for infinite order pseudodifferential operators
- Provided several illustrative examples

## Abstract

We develop a theory of pseudodifferential operators of infinite order for the global classes $\mathcal{S}_{\omega}$ of ultradifferentiable functions in the sense of Bj\"orck, following the previous ideas given by Prangoski for ultradifferentiable classes in the sense of Komatsu. We study the composition and the transpose of such operators with symbolic calculus and provide several examples.