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- W2034396275 abstract "We study the Kolmogorov m -widths d m ( B s α ( L τ , μ ) , L p , μ ) and the linear m -widths δ m ( B s α ( L τ , μ ) , L p , μ ) of the weighted Besov classes B s α ( L τ , μ ) on [ − 1 , 1 ] , where L q , μ , 1 ⩽ q ⩽ ∞ , denotes the L q space on [ − 1 , 1 ] with respect to the measure ( 1 − t 2 ) μ − 1 / 2 d t , μ > 0 . Optimal asymptotic orders of d m ( B s α ( L τ , μ ) , L p , μ ) and δ m ( B s α ( L τ , μ ) , L p , μ ) as m → ∞ are obtained for all 1 ⩽ p , τ ⩽ ∞ . It turns out that in many cases, the orders of d m ( B s α ( L τ , μ ) , L p , μ ) are significantly smaller than the corresponding orders of the best m -term approximation by ultraspherical polynomials, which is somewhat surprising." @default.
- W2034396275 created "2016-06-24" @default.
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- W2034396275 date "2006-03-01" @default.
- W2034396275 modified "2023-09-30" @default.
- W2034396275 title "Kolmogorov and linear widths of weighted Besov classes" @default.
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- W2034396275 doi "https://doi.org/10.1016/j.jmaa.2005.08.046" @default.
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