Approximation of smooth functions on compact two-point homogeneous spaces
| dc.creator | Brown, Gavin | |
| dc.creator | Dai, Feng | |
| dc.date | 2005-09-30 | |
| dc.date.accessioned | 2026-07-07T06:20:32Z | |
| dc.date.available | 2026-07-07T06:20:32Z | |
| dc.description | Estimates of Kolmogorov $n$-widths $d_n(B_p^r, L^q)$ and linear $n$-widths $\da_n(B_p^r, L^q)$, ($1\leq q\leq \infty$) of Sobolev's classes $B_p^r$, ($r>0$, $1\leq p\leq \infty$) on compact two-point homogeneous spaces (CTPHS) are established. For part of $(p, q)\in[1,\infty]\times[1,\infty]$, 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. | |
| dc.identifier | https://arxiv.org/abs/math/0510007 | |
| dc.identifier | http://arxiv.org/abs/math/0510007 | |
| dc.identifier | J. Funct. Anal. 220 (2005), no. 2, 401--423 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95348 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 41A46, 41A17 | |
| dc.title | Approximation of smooth functions on compact two-point homogeneous spaces | |
| dc.type | text |