Tensor products for Gelfand-Shilov and Pilipovi{\'c} distribution spaces

TL;DR

This paper investigates tensor product properties for Gelfand-Shilov and Pilipović distribution spaces, including Fubbini's property, and applies these results to analyze short-time Fourier transforms of these distributions.

Contribution

It establishes fundamental tensor product properties and Fubbini's property for Gelfand-Shilov and Pilipović distributions, extending their analytical framework.

Findings

Tensor products satisfy Fubbini's property for these distributions.

Properties of short-time Fourier transforms are derived from tensor product results.

The work enhances understanding of distribution space interactions and transforms.

Abstract

We show basic properties on tensor products for Gelfand-Shilov distributions and Pilipovi{\'c} distributions. This also includes the Fubbini's property of such tensor products. We also apply the Fubbini property to deduce some properties for short-time Fourier transforms of Gelfand-Shilov and Pilipovi{\'c} distributions.