Abstract :
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.
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