THE RECOVERY OF FUNCTIONS OF PALEY-WIENER CLASS FROM IRREGULAR SAMPLINGS  

作　　者：房艮孙 陈雪冬 

出　　处：《Acta Mathematica Scientia》2002年第4期466-472,共7页数学物理学报（B辑英文版）

基　　金：The project supported by National Natural Science Foundation of China(10071006); Doctoral Programme Foundation of State Education Commission

摘　　要：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]).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]).

关 键 词：tempered spline interpolation Paley-Wienerclass Riesz bases 

分 类 号：O174[理学—数学]