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arXiv · 2505.14041

Moment problems in the Schwartz and Gelfand-Shilov spaces

Andreas Debrouwere
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Abstract

We provide a geometric characterization of the closed sets $K \subseteq \mathbb{R}^d$ such that every real $d$-sequence is the moment sequence of some Schwartz function on $\mathbb{R}^d$ with support in $K$. We obtain a similar result for Gelfand-Shilov spaces. Several illustrative examples are discussed. Our work is inspired by a recent result of Schm\"udgen [Expositiones Math. 43 (2025), 125657], who addressed the analogous problem for Radon measures.

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BibTeXRIS

Andreas Debrouwere. 2025-05-20. Moment problems in the Schwartz and Gelfand-Shilov spaces. https://arxiv.org/abs/2505.14041

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