【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<p <∞确定了Hermitecardinal插值的混淆误差阶的精确估计更多还原

【Abstract】 It 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.更多还原