| 基样条插值的极限性质 |
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| 引用本文： | 陈雪东,房艮孙. 基样条插值的极限性质[J]. 数学杂志, 2000, 20(4): 375-382 |
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| 作者姓名： | 陈雪东 房艮孙 |
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| 作者单位： | 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 |
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| 基金项目： | Supported by the National Natural Science Foundation of China( 1 9671 0 1 2 )，Doctoral Foundation of Chinese Educational Comm |
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| 摘 要： | 本文证明了当m→∞时‖s^(k)mf-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，进而得一了函数类Bπ，p的三个等价的特征刻划。
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| 关 键 词： | 基样条插值 整函数 WHITTAKER级数 极限性质 |
LIMITING BEHAVIOR OF CARDINAL SPLINE INTERPOLATION |
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| CHEN Xue-dong,FANG Gen-sun. LIMITING BEHAVIOR OF CARDINAL SPLINE INTERPOLATION[J]. Journal of Mathematics, 2000, 20(4): 375-382 |
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| Authors: | CHEN Xue-dong FANG Gen-sun |
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| Abstract: | 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∈Bπ,p=Bπ∩Lp(R), and Bπ denotes the subset of all entire functions of exponential type π which are bounded on R, and Sm(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 Bπ,p. |
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| Keywords: | cardinal spline interpolation entire function Whittaker series |
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