Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces - Dorogovtsev, A. A. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
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).