摘要
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≤∞.
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 ofL q(?)), 1 <p=q < ∞, or 11 <p=q < ? ∞.
基金
the National Natural Science Foundation of China (Grant No. 10071006)
the Research Fund for the Doctoral Program of Higher Education.
