Hermite型插值的混淆误差的估计

The Estimation of Aliasing Error of Interpolation of Hermite Type

证明了如果f∈Lp1(R),f′(x)=O(1+|x|)-(1/p-δ)),δ>0且f′在R上任何有限区间上Riemann可积,则‖f-Hσ(f)‖p(R)≤Cpσ-1ωkf′,σ1.其中Hσ(f)是f通过由其样本fkσπk∈Z和f′kσπk∈Z在Lp(R)中的指数2σ型整函数空间B2σ,p中的Her-mite型的插值算子,ωk(f,t):=sup|h|≤t‖Δhkf(x)‖p(R)为函数f的k阶光滑模.

In this paper,it is proved that if f∈L^1_p(R),f′(x)=O((1+|x|)^(-1/p-δ)),δ>0 and f′ is Riemann integrable on every finite interval,then ‖f-H_σ(f)‖_(p(R))≤C_pσ^(-1)w_k(f′,1σ),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.