Ukrainian Mathematical Journal

, Volume 51, Issue 1, pp 66–75

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

  • Authors
  • A. A. Malyarenko
Article

DOI: 10.1007/BF02591915

Cite this article as:
Malyarenko, A.A. Ukr Math J (1999) 51: 66. doi:10.1007/BF02591915
  • 14 Views

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 spaceL2(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.

Copyright information

© Kluwer Academic/Plenum Publishers 1999