Moment problem for algebras generated by a nuclear space
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866917872766287872 |
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| author | Infusino, Maria Kuhlmann, Salma Kuna, Tobias Michalski, Patrick |
| author_facet | Infusino, Maria Kuhlmann, Salma Kuna, Tobias Michalski, Patrick |
| contents | We establish a criterion for the existence of a representing Radon measure for linear functionals defined on a unital commutative real algebra $A$, which we assume to be generated by a vector space $V$ endowed with a Hilbertian seminorm $q$. Such a general criterion provides representing measures with support contained in the space of characters of $A$ whose restrictions to $V$ are $q-$continuous. This allows us in turn to prove existence results for the case when $V$ is endowed with a nuclear topology. In particular, we apply our findings to the symmetric tensor algebra of a nuclear space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12949 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Moment problem for algebras generated by a nuclear space Infusino, Maria Kuhlmann, Salma Kuna, Tobias Michalski, Patrick Functional Analysis Probability 44A60, 46M40, 28C20 We establish a criterion for the existence of a representing Radon measure for linear functionals defined on a unital commutative real algebra $A$, which we assume to be generated by a vector space $V$ endowed with a Hilbertian seminorm $q$. Such a general criterion provides representing measures with support contained in the space of characters of $A$ whose restrictions to $V$ are $q-$continuous. This allows us in turn to prove existence results for the case when $V$ is endowed with a nuclear topology. In particular, we apply our findings to the symmetric tensor algebra of a nuclear space. |
| title | Moment problem for algebras generated by a nuclear space |
| topic | Functional Analysis Probability 44A60, 46M40, 28C20 |
| url | https://arxiv.org/abs/2301.12949 |