Approximation of smooth functions on compact two-point homogeneous spaces

2005/09/30 by Gavin Brown, Feng Dai
Mathematics · #math.CA #math.AP #msc:41A46 #msc:41A17

paper · pdf

published as J. Funct. Anal. 220 (2005), no. 2, 401--423

arxiv created 2005/09/30 · arxiv updated 2009/12/01

Abstract

Estimates of Kolmogorov n-widths d_n(B_p^r, L^q) and linear n-widths \da_n(B_p^r, L^q), (1≤ q≤ ∞) of Sobolev's classes B_p^r, (r>0, 1≤ p≤ ∞) on compact two-point homogeneous spaces (CTPHS) are established. For part of (p, q)∈[1,∞]×[1,∞], 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.

Cited by

• Divergence-free interpolation of tangential vector fields via matrix-valued kernels