基样条插值的极限性质(英文)  

LIMITING BEHAVIOR OF CARDINAL SPLINE INTERPOLATION

作　　者：陈雪东 房艮孙[2] 

机构地区：[1]云南楚雄师范专科学校数学系,楚雄675000 [2]北京师范大学数学系,北京100875

出　　处：《数学杂志》2000年第4期375-382,共8页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China( 1 9671 0 1 2 ) ;Doctoral Foundation of Chinese Educational Comm

摘　　要：本文证明了当 m→∞时‖ s( k)m f- f( k) ‖ p→ 0 ( 1 <p<∞ ,k=0 ,1 ,2… )的充要条件是 f∈Bπ,p,其中 Bπ,p=Bπ∩ Lp( R) ,Bπ 表示指数 π型的整函数在 R上限制为有界函数所构成的集合 ,而Smf是在整数点对 f插值的唯一确定的 m-1次基样条 .进而得到了函数类 Bπ,p的三个等价的特征刻划 .In this paper, we show that the necessary and sufficient conditions for which ‖S (k) m(f)F-f (k) ‖ p→0 as m→∞,1<p<∞,k=0,1,2,…, are f∈B π,p =B π∩L p(R), and B π denotes the subset of all entire functions of exponential type π which are bounded on R, and S m(f) is the unique cardinal spline of degree m-1 interpolationg to f at integers. Moreover, we obtain three equivalent forms about the characterization of the class of functions B π,p .

关 键 词：基样条插值 整函数 WHITTAKER级数 极限性质 

分 类 号：O174.41[理学—数学] O174.52[理学—基础数学]