Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces

• Date: 2000
• Main Authors: Dorogovtsev, A. A., Дороговцев, А. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4526
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the structure of orthogonal polynomials in the space L 2(B, μ) for a probability measure μ on a Banach space B. These polynomials are described in terms of Hilbert–Schmidt kernels on the space of square-integrable linear functionals. We study the properties of functionals of this sort. C...