Convergent star product algebras on "ax+b"

TL;DR

This paper introduces non-tempered function spaces on the ax+b Lie group that remain stable under a specific convergent star product, expanding the understanding of algebraic structures with exponential growth.

Contribution

It defines new non-tempered function spaces on ax+b that are stable under a convergent star product, advancing the study of algebraic structures with exponential growth.

Findings

Defined non-tempered function spaces on ax+b

Established stability under a convergent star product

Extended algebraic frameworks for exponential growth functions

Abstract

We define non-tempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product.