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


  • A. A. Malyarenko

DOI: 10.1007/BF02591915

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


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