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Distribution of polynomials in many variables and Nikolskii-Besov spaces. (English) Zbl 1423.28039

Summary: We discuss recent results and open problems connected with distributions of polynomials in many or infinitely many variables on spaces with Gaussian measures and Nikolskii-Besov spaces of fractional smoothness related to such distributions.

MSC:

28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
60H07 Stochastic calculus of variations and the Malliavin calculus
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