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- W2011691693 abstract "We present sharp bounds on the Kolmogorov probabilistic (N,δ)-width and p-average N-width of multivariate Sobolev space with mixed derivative MW2r(Td),r=(r1,…,rd),1/2<r1=⋯=rν<rν+1⩽⋯⩽rd, equipped with a Gaussian measure μ in Lq(Td), that is dN,δ(MW2r(Td),μ,Lq(Td))≍(N−1lnν−1N)r1+(ρ−1)/2(ln(ν−1)/2N)1+(1/N)ln(1/δ),d(a)N(MW2r(Td),μ,Lq(Td))p≍(N−1lnν−1N)r1+(ρ−1)/2(ln(ν−1)/2N),where 1<q<∞,0<p<∞, and ρ>1 is depending only on the eigenvalues of the correlation operator of the measure μ (see (4))." @default.
- W2011691693 created "2016-06-24" @default.
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- W2011691693 date "2004-12-01" @default.
- W2011691693 modified "2023-09-26" @default.
- W2011691693 title "Probabilistic and average widths of multivariate Sobolev spaces with mixed derivative equipped with the Gaussian measure" @default.
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- W2011691693 doi "https://doi.org/10.1016/j.jco.2004.04.001" @default.
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