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).
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Dorogovtsev, A.A. Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces. Ukrainian Mathematical Journal 52, 1366–1379 (2000). https://doi.org/10.1023/A:1010371817382
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DOI: https://doi.org/10.1023/A:1010371817382