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 L-q (R), 2 < q < infinity, from its values on irregularly distributed dis...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 L-q (R), 2 < q < infinity, from its values on irregularly distributed discrete sampling set {t(j)}(j)is an element ofz as limits of polynomial spline interpolation when the order of the splines goes to infinity, where {t(j)}(jis an element ofz) is a real sequence such that {e(j)(it)(zeta)} j(is an element ofz) constitutes a Riesz basis for L-2([-pi, pi]).展开更多
基金The project supported by National Natural Science Foundation of China(10071006) Doctoral Programme Foundation of State Education Commission
文摘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 L-q (R), 2 < q < infinity, from its values on irregularly distributed discrete sampling set {t(j)}(j)is an element ofz as limits of polynomial spline interpolation when the order of the splines goes to infinity, where {t(j)}(jis an element ofz) is a real sequence such that {e(j)(it)(zeta)} j(is an element ofz) constitutes a Riesz basis for L-2([-pi, pi]).
