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• W2017788193 abstract "A generalized polynomial is a real-valued function which is obtained from conventional polynomials by the use of the operations of addition, multiplication, and taking the integer part; a generalized polynomial mapping is a vector-valued mapping whose coordinates are generalized polynomials. We show that any bounded generalized polynomial mapping u: Zd → Rl has a representation u(n) = f(ϕ(n)x), n ∈ Zd, where f is a piecewise polynomial function on a compact nilmanifold X, x ∈ X, and ϕ is an ergodic Zd-action by translations on X. This fact is used to show that the sequence u(n), n ∈ Zd, is well distributed on a piecewise polynomial surface $mathcal{S}subsetmathbf{R}^{l}$ (with respect to the Borel measure on $mathcal{S}$ that is the image of the Lebesgue measure under the piecewise polynomial function defining $mathcal{S}$). As corollaries we also obtain a von Neumann-type ergodic theorem along generalized polynomials and a result on Diophantine approximations extending the work of van der Corput and of Furstenberg–Weiss." @default.
• W2017788193 created "2016-06-24" @default.
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• W2017788193 date "2007-01-01" @default.
• W2017788193 modified "2023-09-25" @default.
• W2017788193 title "Distribution of values of bounded generalized polynomials" @default.
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• W2017788193 doi "https://doi.org/10.1007/s11511-007-0015-y" @default.
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