带导数的Whittaker-Shannon-Kotelnikov样本定理  

Whittaker-Shannon-Kotelnikov Sampling Theorem with Derivatives

作　　者：李冱岸[1] 陈佳[1] 李婧淑 

机构地区：[1]北方工业大学理学院,北京100041

出　　处：《数学的实践与认识》2014年第12期313-320,共8页Mathematics in Practice and Theory

摘　　要：证明了在Lp(R)尺度下,Fourier变换具有紧支集[—σ,σ]的带有限函数类B3_(σ,p)可以由原函数及带导数序列{f(κπ/δ)}、{f'(κπ/δ)}以及{f"(κπ/δ)},κ∈R完全重构,进一步计算了,当f在L_r^p(R)中时的逼近阶.In this paper we prove that, denote by B3σ,p the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [-σ,σ], then a function in B3a,p can be reconstructed in Lp（a） by its sampling sequences{f（kπ/δ）}、{f′（kπ/δ））and {f″（kπ/δ）},in Lp（R）, Further, we calculate the order of approximation.

关 键 词：带有限函数 重构 逼近阶 

分 类 号：O174.41[理学—数学]