On the Moment Functionals with Signed Representing Measures
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910447961112576 |
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| author | Schmüdgen, Konrad |
| author_facet | Schmüdgen, Konrad |
| contents | Suppose that $\sA$ is a finitely generated commutative unital real algebra and $K$ is a closed subset of the set $\hat{A}$ of characters of $\sA$. We study the following problem: When is {\it each} linear functional $L:{\sA} \to \dR$ an integral with respect to some signed Radon measure on $\hat{\sA}$ supported by the set $K$? A complete characterization of the sets $K$ and algebras $\sA$ by necessary and sufficient conditions is given. The result is applied to the polynomial algebra $\dR[x_1,\dots,x_d]$ and subsets $K$ of $\dR^d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08899 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Moment Functionals with Signed Representing Measures Schmüdgen, Konrad Functional Analysis 44 A 60 Suppose that $\sA$ is a finitely generated commutative unital real algebra and $K$ is a closed subset of the set $\hat{A}$ of characters of $\sA$. We study the following problem: When is {\it each} linear functional $L:{\sA} \to \dR$ an integral with respect to some signed Radon measure on $\hat{\sA}$ supported by the set $K$? A complete characterization of the sets $K$ and algebras $\sA$ by necessary and sufficient conditions is given. The result is applied to the polynomial algebra $\dR[x_1,\dots,x_d]$ and subsets $K$ of $\dR^d$. |
| title | On the Moment Functionals with Signed Representing Measures |
| topic | Functional Analysis 44 A 60 |
| url | https://arxiv.org/abs/2405.08899 |