基样条与整函数的极限性质  

The Limit Properties of Entire Functions and Cardinal Spline

作　　者：陈雪东 

机构地区：[1]云南楚雄师范专科学校数学系,云南楚雄675000

出　　处：《工科数学》2000年第2期32-34,共3页Journal of Mathematics For Technology

摘　　要：本文证明了‖smf-f‖ p→ 0 ( m→∞ )的必要条件是 f∈ Bπ,p,其中 Bπ,p=Bπ∩ Lp( R) ,Bπ表示指数 π型的整函数在R上限制是有界函数所构成的集合 ,smf 是在整数点对 f 插值的唯一确定的 m-1次基样条 .In this paper we show that the necessory condition for which ‖ s mf-f‖ p→0(m→∞) is f∈B π,p , where 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 mf is the unique cardinal spline of degree m-1 interpolating to f at integers. Moreover, we obtain an equivalent form about the characterization of the class of functions B π,p .

关 键 词：基样条 整函数 插值 极限性质 有界函数 

分 类 号：O174.41[理学—数学] O174.52[理学—基础数学]