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Two generalizations of Mehler’s formula in white noise analysis
Technische Universität Kaiserslautern, Germany.ORCID iD: 0000-0002-8400-0416
Technische Universität Kaiserslautern, Germany.
2023 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 95, no 4, p. 501-520Article in journal (Refereed) Published
Abstract [en]

Mehler's formula is an important tool in Gaussian analysis. In this article, we study two generalizations of Mehler's formula for the Ornstein–Uhlenbeck semigroup, i.e. the semigroup generated by the number operator. The first generalization leads to transformation groups which have as infinitesimal generator a perturbation of the number operator with suitable integral kernel operators, which are well studied in white noise analysis. For the second one, we characterize the complex Hida measures for which a version of Mehler's formula for the Ornstein–Uhlenbeck semigroup can be extended to. We apply this result to the Feynman integrand for a quadratic potential. Here the time independent eigenstates of the considered transformation groups and the time evolution of eigenvalues are provided.

Place, publisher, year, edition, pages
Elsevier, 2023. Vol. 95, no 4, p. 501-520
National Category
Probability Theory and Statistics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-124514DOI: 10.1080/17442508.2022.2089039ISI: 000814174700001Scopus ID: 2-s2.0-85132349129OAI: oai:DiVA.org:lnu-124514DiVA, id: diva2:1802897
Available from: 2023-10-06 Created: 2023-10-06 Last updated: 2023-10-17Bibliographically approved

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Bock, Wolfgang

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