On Gelfand-Shilov spaces of type $W$

TL;DR

This paper explores generalized spaces of infinitely differentiable functions on Euclidean space, extending Gelfand-Shilov spaces, and establishes Paley-Wiener type theorems for these spaces.

Contribution

It introduces broader classes of function spaces beyond classical Gelfand-Shilov spaces and proves Paley-Wiener theorems for them, expanding the theoretical framework.

Findings

Established Paley-Wiener theorems for new function spaces

Extended the class of infinitely differentiable function spaces

Provided foundational results for analysis on generalized Gelfand-Shilov spaces

Abstract

Spaces of infinitely differentiable functions on ${\mathbb R}^n$ (more general than Gelfand-Shilov spaces of type $W_M$) are considered in the article. Paley-Wiener type theorems are obtained.