Approximation of smooth functions on compact two-point homogeneous spaces

By Gavin Brown, Feng Dai. 2005

143 citations recorded by the source corpus.

Estimates of Kolmogorov n-widths dn(Bpr,Lq) and linear n-widths δn(Bpr,Lq), (1⩽q⩽∞) of Sobolev's classes Bpr, (r>0, 1⩽p⩽∞) on compact two-point homogeneous spaces (CTPHS) are established. For part of (p,q)∈[1,∞]×[1,∞], sharp orders of dn(Bpr,Lq) or δn(Bpr,Lq) were obtained by Bordin et al. (J. Funct. Anal. 202(2) (2003) 307). In this paper, we obtain the sharp orders of dn(Bpr,Lq) and δn(Bpr,Lq) for all the remaining (p,q). Our proof is based on positive cubature formulas and Marcinkiewicz–Zygmund-type inequalities on CTPHS.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c65e1069116664b7b5511316acf8933150b4569a

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In Applied Mathematics

1. Pencho Petrushev
2. Yuan Xu
3. Feng Dai
4. Francis J. Narcowich
5. Joseph D. Ward
6. Daryl Geller
7. Azita Mayeli
8. Gerard Kerkyacharian

In Numerical Analysis

1. Feng Dai
2. Pencho Petrushev
3. Yuan Xu

Citations in the corpus

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