Probabilistic and average linear widths of Sobolev space with Gaussian measure

نویسندگان

  • Gensun Fang
  • Peixin Ye
چکیده

E-mail: [email protected] Abstract: We determine the exact order of the p-average linear n-widths λ n (W r 2 , μ, Lq)p, 1 ≤ q < ∞, 0 < p <∞, of the Sobolev space W r 2 equipped with a Gaussian measure μ in the Lq-norm. Moreover, we also calculate the probabilistic linear (n, δ)-widths and p-average linear n-widths of the finitedimensional space R with the standard Gaussian measure in l q , i.e.,

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Probabilistic linear widths of Sobolev space with Jacobi weights on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[-1,1]$\end{document}[−1,1]

*Correspondence: [email protected] School of Mathematical and Statistics, Zaozhuang University, Zaozhuang, 277160, China Abstract Optimal asymptotic orders of the probabilistic linear (n,δ)-widths of λn,δ (Wr 2,α,β ,ν , Lq,α,β ) of the weighted Sobolev spaceW r 2,α,β equipped with a Gaussian measure ν are established, where Lq,α,β , 1≤ q≤∞, denotes the Lq space on [–1, 1] with respect to the me...

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عنوان ژورنال:
  • J. Complexity

دوره 19  شماره 

صفحات  -

تاریخ انتشار 2003