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Moment problem for algebras generated by a nuclear space

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2024

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Advances in Mathematics. Elsevier BV. 2024, 448, 109677. ISSN 0001-8708. eISSN 1090-2082. Verfügbar unter: doi: 10.1016/j.aim.2024.109677

Zusammenfassung

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.

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Fachgebiet (DDC)
510 Mathematik

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Moment problem, Infinite dimensional moment, Nuclear space, Projective limit, Prokhorov's condition

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ISO 690INFUSINO, Maria, Salma KUHLMANN, Tobias KUNA, Patrick MICHALSKI, 2024. Moment problem for algebras generated by a nuclear space. In: Advances in Mathematics. Elsevier BV. 2024, 448, 109677. ISSN 0001-8708. eISSN 1090-2082. Verfügbar unter: doi: 10.1016/j.aim.2024.109677
BibTex
@article{Infusino2024-06Momen-70618,
  year={2024},
  doi={10.1016/j.aim.2024.109677},
  title={Moment problem for algebras generated by a nuclear space},
  volume={448},
  issn={0001-8708},
  journal={Advances in Mathematics},
  author={Infusino, Maria and Kuhlmann, Salma and Kuna, Tobias and Michalski, Patrick},
  note={Article Number: 109677}
}
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