Limit theorems in spline approximation

In this paper we establish new asymptotic relations of the form [graphics] where E(f, S(h),m, L(p)(R)) and E(f, B(pi/h), L(p)(R)) are the errors of best approximation of a function in L(p)(R), 1 <= p <= infinity, by splines of order m with breakpoints {kh}(k=-infinity)(infinity) functions of exponential type pi/h, respectively. Approximation and interpolation of entire functions of exponential type by splines of high order is discussed as well. (c) 2005 Elsevier Inc. All rights reserved.