Moment problems in the Schwartz and Gelfand-Shilov spaces

2025/05/20 by Andreas Debrouwere, Debrouwere, Andreas
Mathematics · Physics and Astronomy · #44A60 #46E10 #FOS: Mathematics #Functional Analysis (math.FA) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.14041

openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a geometric characterization of the closed sets K ⊆ ℝ^d such that every real d-sequence is the moment sequence of some Schwartz function on 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.

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