Truncation and aliasing errors for Whittaker-Kotelnikov-Shannon sampling expansion

摘要

Let BΩp , 1 ≤ p < ∞, be the space of all bounded functions from Lp(R) which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series based on local sampling are derived for functions f ∈ BΩp 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(Wpr(R)) are determined up to a logarithmic factor.