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 i...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 < ? ∞.展开更多
基金the National Natural Science Foundation of China (Grant No. 10071006) the Research Fund for the Doctoral Program of Higher Education.
文摘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 < ? ∞.
