Linear widths of a multivariate function space equipped with a Gaussian measure

  • Authors:

  • Chen Guanggui;Fang Gensun

  • Affiliations:

  • School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China and School of Computers and Mathematical-Physical Science, XiHua University, Chengdu, China;School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2005

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Abstract

We determine the asymptotic values on the linear probabilistic (N,@d)-widths and linear p-average N-widths of the space of multivariate functions with bounded mixed derivative MW"2^r(T^d), r=(r"1,...,r"d), 1/21 depends only on the eigenvalues of the correlation operator of the measure @m (see (4)). If the dimension d=2, then the asymptotic exact order of probabilistic linear widths of MW"2^r(T^d) with the Gaussian measure @m in the L"q(T^d) space for the cases q=1, 2