R上由指数型整函数的Hermite型插值的收敛性

THE CONVERGENCE OF HERMITE TYPE INTERPOLATION BY ENTIRE FUNCTIONS OF EXPONENTIAL TYPE ON R

证明了如果f∈L1p(R) ,f′(x) =O(1(1+|x|) 1/p+δ) ,δ >0 ,且f′在R的任何有限区间上Riemann可积 ,则limσ→∞‖f-Hσ(f)‖p(R) =0 ,其中Hσ(f)是f通过由其样本 {f(kπσ) } k∈Z和 {f′(kπσ) }k∈Z在Lp(R)中的指数 2σ型整函数空间B2σ,p中的

It is proved that if f∈L 1 p(R),f′(x)=O((1+|x|) 1/p+δ) -1),δ>0, and f′ is Riemann integralbe on every finite interval, then %lim%σ→∞‖f-H σ(f)‖ p(R)=0, where H σ(f) is the Hermite type interpolation of f via its sampling sequences ｛f(kπ/σ)｝ k∈Z and ｛f′(kπ/σ)｝ k∈Z and B 2σ,p is the subspace L p(R) of entire functions of exponential 2σ type.