Moment problems in the Schwartz and Gelfand-Shilov spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912383125946368 |
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| author | Debrouwere, Andreas |
| author_facet | Debrouwere, Andreas |
| contents | 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 Schmüdgen [Expositiones Math. 43 (2025), 125657], who addressed the analogous problem for Radon measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moment problems in the Schwartz and Gelfand-Shilov spaces Debrouwere, Andreas Functional Analysis 44A60, 46E10 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 Schmüdgen [Expositiones Math. 43 (2025), 125657], who addressed the analogous problem for Radon measures. |
| title | Moment problems in the Schwartz and Gelfand-Shilov spaces |
| topic | Functional Analysis 44A60, 46E10 |
| url | https://arxiv.org/abs/2505.14041 |