The main result of this paper asserts that if a function f is in the class Bπ,p, 1＜p＜∞; that is, those p-integrable functions whose Fourier transforms are supported in the interval ［-π, π］, then f and its derivatives f(j), j=1, 2, …， can be recovered from its sampling sequence ｛f(k)｝ via the cardinal interpolating spline of degree m in the metric of Lq(R), 1＜p=q＜∞, or 1＜p＜q≤∞.
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 ≤ ∞, from its values on irregularly distributed discrete sampling set {tj}j∈z as limits of polynomial spline interpolation when the order of the splines goes to infinity, where {tj}j∈z is a real sequence such that {eifj(?)}j∈z constitutes a Riesz basis for L2([-π,π]).
