Approximation of smooth functions on compact two-point homogeneous spaces |
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| Authors: | Gavin Brown Feng Dai |
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| Institution: | aUniversity of Sydney, NSW 2006, Australia;bDepartment of Mathematical and Statistical Sciences, Central Academic Building 632, University of Alberta, Edmonton, Alberta Canada T6G 2G1 |
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| Abstract: | Estimates of Kolmogorov n-widths and linear n-widths , (1q∞) of Sobolev's classes , (r>0, 1p∞) on compact two-point homogeneous spaces (CTPHS) are established. For part of (p,q)1,∞]×1,∞], sharp orders of or were obtained by Bordin et al. (J. Funct. Anal. 202(2) (2003) 307). In this paper, we obtain the sharp orders of and for all the remaining (p,q). Our proof is based on positive cubature formulas and Marcinkiewicz–Zygmund-type inequalities on CTPHS. |
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| Keywords: | Compact two-point homogeneous spaces n-widths Marcinkiewicz– Zygmund inequalities Positive cubature formulas |
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