Limit theorems in spline approximation

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