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
The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for ...The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation.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 < ? ∞.
基金Projcct supported by the Natural Science Foundation of China (Grant No. 10371009 ) of Beijing Educational Committee (No. 2002KJ112).
文摘The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation.
