Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces

Abstract

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. Certain probability measures are regarded as generalized functionals on the space (B, μ).