HERMITE型导数样本定理和Sobolev类上的混淆误差  

SAMPLING THEOREM OF HERMITE TYPE AND ALIASING ERROR ON THE SOBOLEV CLASS OF FUNCTIONS

作　　者：李冱岸[1] 房艮孙[1] 

机构地区：[1]北京师范大学数学系,北京100875

出　　处：《北京师范大学学报（自然科学版）》2004年第3期315-319,共5页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目 (10 3 710 0 9)

摘　　要：证明了 :如果函数f属于带有限函数类B2σ ,p,1<p <∞ ,即 p 次可积且Fourier变换支集包含于闭区间 [-σ ,σ]的函数全体 ,则它能在Lp(R)范意义下由其样本序列 { f(kπ/σ) } k∈Z,{ f′(kπ/σ) } k∈Z通过Hermitecardinal插值完全重构 ,并且对 f∈Lrp(R) ,1<pIt is shown that a function f is in the bandlimited class B 2σ,p ,1<p<∞ , that is, those p integrable functions whose Fourier transform is supported in the interval [- σ, σ ], then it can be reconstructed in the sense of L p (R) norm by its sampling sequences ｛f(k π /σ)｝ k∈Z and ｛ f′(k π /σ)｝ k∈Z via the Hermite cardinal interpolation . Moreover, if f belongs to L r p(R),1<p<∞, then the exact order of its aliasing error is determined.

关 键 词：Marcinkiewicz型不等式 带有限函数 导数样本 Sobolev函数类 混淆误差 

分 类 号：O175.3[理学—数学]