带二阶导数的插值定理

Interpolation Theorem With the Two Order Derivatives

用B_(δ,p)(1<P<∞)表示P次可积Fourier变換具有紧支集[-δ,δ]的带有限函数。证明了对于B_(3δ,p)中的函数,可以在L_p(R)尺度下,由序列{f(κπ/δ)},{f'(κπ/δ)}以及{f''(κπ/δ)}的Hermite型插值进行重构.

Denote by Bσ,p（1〈p〈∞） the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [-σ, σ]. It is shown that a function in B3σ,p（1 p 〈 ∞） can be reconstructed ill Lp（R） by its sampling sequences {f（κπ/δ）},{f＇（κπ/δ）}and {f＂（κπ/δ）} using the Hermite cardinal interpolation.