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Approximation of smooth functions on compact two-point homogeneous spaces | | Gavin Brown
; Feng Dai
; | | Date: |
1 Oct 2005 | | Journal: | J. Funct. Anal. 220 (2005), no. 2, 401--423 | | Subject: | Classical Analysis and ODEs; Analysis of PDEs MSC-class: 41A46, 41A17 | math.CA math.AP | | Abstract: | Estimates of Kolmogorov $n$-widths $d_n(B_p^r, L^q)$ and linear $n$-widths $da_n(B_p^r, L^q)$, ($1leq qleq infty$) of Sobolev’s classes $B_p^r$, ($r>0$, $1leq pleq infty$) on compact two-point homogeneous spaces (CTPHS) are established. For part of $(p, q)in[1,infty] imes[1,infty]$, sharp orders of $d_n(B_p^r, L^q)$ or $da_n (B_p^r, L^q) $ were obtained by Bordin, Kushpel, Levesley and Tozoni in a recent paper `` J. Funct. Anal. 202 (2) (2003), 307--326’’. In this paper, we obtain the sharp orders of $d_n(B_p^r, L^q)$ and $da_n (B_p^r, L^q)$ for all the remaining $ (p,q)$. Our proof is based on positive cubature formulas and Marcinkiewicz-Zygmund type inequalities on CTPHS. | | Source: | arXiv, math.CA/0510007 | | Services: | Forum | Review | PDF | Favorites | |
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