Pseudo-differential calculus in anisotropic Gelfand-Shilov setting

TL;DR

This paper investigates pseudo-differential operators with anisotropic exponential growth symbols and establishes their mapping properties and invariance in Gelfand-Shilov spaces, advancing understanding of their algebraic structure.

Contribution

It introduces new classes of pseudo-differential operators with anisotropic exponential growth symbols and analyzes their properties in Gelfand-Shilov spaces.

Findings

Proved mapping properties of these operators on Gelfand-Shilov spaces.

Established algebraic and invariance properties of the operator classes.

Extended pseudo-differential calculus in anisotropic Gelfand-Shilov setting.

Abstract

We study some classes of pseudo-differential operators with symbols $a$ admitting anisotropic exponential growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces of type S. Moreover, we deduce algebraic and certain invariance properties of these classes.