Characterization of nuclearity for Beurling-Bj\"{o}rck spaces

TL;DR

This paper characterizes the nuclearity of Beurling-Björck spaces based on their defining weight functions, providing a deeper understanding of their functional-analytic properties.

Contribution

It offers a new characterization of nuclearity for Beurling-Björck spaces in terms of weight functions, advancing the theoretical understanding of these spaces.

Findings

Nuclearity conditions are explicitly linked to weight functions.

Provides criteria for nuclearity in Beurling-Björck spaces.

Enhances the theoretical framework for analyzing these function spaces.

Abstract

We characterize the nuclearity of the Beurling-Bj\"{o}rck spaces $\mathcal{S}^{(\omega)}_{(\eta)}(\mathbb{R}^d)$ and $\mathcal{S}^{\{\omega\}}_{\{\eta\}}(\mathbb{R}^d)$ in terms of the defining weight functions $\omega$ and $\eta$.