A projective description of generalized Gelfand-Shilov spaces of Roumieu type

TL;DR

This paper offers a projective framework for generalized Gelfand-Shilov spaces of Roumieu type, encompassing classical Gelfand-Shilov and weighted ultradifferentiable function spaces, enhancing their theoretical understanding.

Contribution

It introduces a new projective description for these spaces, broadening the analytical tools available for their study.

Findings

Provides a unified projective description for Gelfand-Shilov spaces

Extends results to weighted ultradifferentiable function spaces

Enhances the theoretical framework for analyzing these function spaces

Abstract

We provide a projective description for a class of generalized Gelfand-Shilov spaces of Roumieu type. In particular, our results apply to the classical Gelfand-Shilov spaces and weighted $L^\infty$-spaces of ultradifferentiable functions of Roumieu type.