有限带L_p函数非正规样本表示的截断误差界

TRUNCATION ERROR BOUNDS FOR IRREGULAR SAMPLIMG EXPANSIONS OF BANDLIMITED L_p-FUNCTIONS

令 Bσ,p,1<p <∞表示 Lp 中有限带函数 (带落在 [-σ,σ]内 )的全体 .由著名的 Whit-taker- Kotelnikw- Shannon样本定理 ,一切 Bσ,p中的函数 f可以由无限多个样本点重构 ,即f(x) =∑k∈ Zf(kπσ) sinσ(x- kπ/σ)σ(x- kπ/σ) .进一步的研究表明 f∈ Bσ,p可以由某些非正规样本点重构 .但是在实际应用上 ,只能记录和处理有限多个样本点 ,故研究截断误差估计是重要的 .通过研究给出了在某些条件下由正规样本点和非正规样本点所确定的 Lp

Let B σ,p ,1<p<∞ denote the space of all L p functions that are bandlimited to . The well known Whittaker Kotelnikov Shannon sampling theorem states that every f∈B σ,p can be reconstructed by its infinitely many sampling points, i.e., f(x)=∑k∈Zf(k π σ) sin (σ(x-k π /σ))σ(x-k π /σ), x∈R. Furthermore, f∈B σ,p can be reconstructed by irregular sampling points. But, in practice, only a finite number of samples can be measured and stored, so one would like to study the truncation error. In the cases of the regular sampling points and the irregular ones, the uniform bounds are given for the truncation error of bandlimited L p functions which satisfy some conditions.