Derivative Uniform Sampling via Weierstrass σ(z). Truncation Error Analysis in
نویسندگان
چکیده
منابع مشابه
DERIVATIVE UNIFORM SAMPLING VIA WEIERSTRASS σ ( z ) . TRUNCATION ERROR
In the entire functions space [ 2, πq 2s2 ) consisting of at most second order functions such that their type is less than πq/(2s) it is valid the qorder derivative sampling series reconstruction procedure, reading at the von Neumann lattice {s(m + ni)| (m,n) ∈ Z2} via the Weierstrass σ(·) as the sampling function, s > 0. The uniform convergence of the sampling sums to the initial function is p...
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(see [9] and [10]). Throughout this work, we assume that the function satis®es the following conditions: (i) j xj cons: jB xj=jxj1"; where " 0 and jB xj is bounded and 1-periodic function on R. (ii) P n2Z n eÿin converges absolutely to a function that has no zeros on ÿ ; . It is known that conditions (i) and (ii) imply that fK x; n; n 2 Zg is a Riesz basis on V , with a unique biort...
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Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker–Kotel'nikov–Shannon (WKS) sampling restoration sum for Bernstein function classes B q π,d , q > 1, d ∈ N, when the decay rate of the sampled functions is unknown. The case of regular sampling is discussed. Extremal properties of related series of sinc functions are investigated.
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ژورنال
عنوان ژورنال: gmj
سال: 2001
ISSN: 1572-9176,1072-947X
DOI: 10.1515/gmj.2001.129