Moment problems related to intrinsic characterizations of the moment functionals
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909946877050880 |
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| author | Atanasiu, Dragu |
| author_facet | Atanasiu, Dragu |
| contents | In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we obtain a characterization of a moment functional on a product of symmetric intervals, in which we do not assume that the functional is positive semidefinite but positive on a semiring of A, and a characterization of a moment functional that is a solution to the moment problem on a product of arbitrary intervals. We also prove a Positivstellensatz for an archimedean cone, which is neither a quadratic module nor a semiring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09751 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moment problems related to intrinsic characterizations of the moment functionals Atanasiu, Dragu Functional Analysis 43A35, 44A60 In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we obtain a characterization of a moment functional on a product of symmetric intervals, in which we do not assume that the functional is positive semidefinite but positive on a semiring of A, and a characterization of a moment functional that is a solution to the moment problem on a product of arbitrary intervals. We also prove a Positivstellensatz for an archimedean cone, which is neither a quadratic module nor a semiring. |
| title | Moment problems related to intrinsic characterizations of the moment functionals |
| topic | Functional Analysis 43A35, 44A60 |
| url | https://arxiv.org/abs/2410.09751 |