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Truncation and aliasing errors for Whittaker-Kotelnikov-Shannon sampling expansion
Authors:Pei-xin Ye  Zhan-jie Song
Affiliation:1. School of Mathematics and LPMC, Nankai University, Tianjin, 300071, China
2. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, China
Abstract:Let B ?? p , 1 ?? p < ??, be the space of all bounded functions from L p (?) which can be extended to entire functions of exponential type ??. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series based on local sampling are derived for functions f ?? B ?? p without decay assumption at infinity. Then the optimal bounds of the aliasing error and truncation error of Whittaker-Kotelnikov-Shannon expansion for non-bandlimited functions from Sobolev classes U(W p r (?)) are determined up to a logarithmic factor.
Keywords:Whittaker-Kotelnikov-Shannon theorem   localized sampling   truncation error   aliasing error  Sobolev class.
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