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Local properties of gaussian random fields on compact symmetric spaces and theorems of the Jackson-Bernstein type

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Abstract

We consider local properties of smaple functions of Gaussian isotropic random fields on compact Riemannian symmetric spacesM of rank 1. We give conditions under which the sample functions of a field almost surely possess logarithmic and power modulus of continuity. As a corollary, we prove a theorem of the Bernstein type for optimal approximations of functions of this sort by harmonic polynomials in the metric of the spaceL 2(M). We use theorems of the Jackson-Bernstein-type to obtain sufficient conditions for the sample functions of a field to almost surely belong to the classes of functions associated with the Riesz and Cesàro means.

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Authors
  1. A. A. Malyarenko
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Additional information

International Mathematical Center, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 60–68, January, 1999.

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Malyarenko, A.A. Local properties of gaussian random fields on compact symmetric spaces and theorems of the Jackson-Bernstein type. Ukr Math J 51, 66–75 (1999). https://doi.org/10.1007/BF02591915

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  • DOI: https://doi.org/10.1007/BF02591915

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