Limit theorems in spline approximation

In this paper we establish new asymptotic relations of the form lim m→∞E f,Sh,m,Lp(R) = E f,Bπ/h,Lp(R) , where E(f,Sh,m,Lp(R)) and E(f,Bπ/h,Lp(R)) are the errors of best approximation of a function f in Lp(R), 1 p ∞, by splines of order m with breakpoints {kh}∞ k=−∞,h > 0, and by entire functions of exponential type π/h, respectively. Approximation and interpolation of entire functions of exponential type by splines of high order is discussed as well. © 2005 Elsevier Inc. All rights reserved