Truncation and aliasing errors for Whittaker-Kotelnikov-Shannon sampling expansion |
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Authors: | Pei-xin Ye Zhan-jie Song |
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Affiliation: | 1. School of Mathematics and LPMC, Nankai University, Tianjin, 300071, China 2. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, China
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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. |
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Keywords: | Whittaker-Kotelnikov-Shannon theorem localized sampling truncation error aliasing error Sobolev class. |
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