Approximation of Densities of Absolutely Continuous Components of Measures in a Hilbert Space Using the Ornstein-Uhlenbeck Semigroup

• Date: 2004
• Main Authors: Rudenko, A. V., Руденко, А. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3872
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study the behavior of measures obtained as a result of the action of the Ornstein-Uhlenbeck semigroup T t associated with the Gaussian measure μ on an arbitrary probability measure ν in a separable Hilbert space as t → 0+. We prove that the densities of the parts of T t ν absolutely continuous...