Abstract
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)) 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.
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