关键词: Tempered spline interpolation, Paley-Wienerclass, Riesz bases

Abstract:

It is shown that a function f which is in the classical Paley-Wiener class,and its k-th derivative f(k) can be recovered in the metric Lq(R), 2 < q  1, from its values on irregularly distributed discrete sampling set {tj}j2Z as limits of polynomial spline interpolation when the order of the splines goes to infinity, where {tj}j2Z is a real sequence such that {eitj}j2Z constitutes a Riesz basis for L2([−, ]).

Key words: Tempered spline interpolation, Paley-Wienerclass, Riesz bases