Best Approximations by Smooth Functions
نویسنده
چکیده
THEOREM 1.1 (U. Sattes). Let r > 2 and g E C[O, l]\B$,‘. Then f”EB$’ is a best approximation to g, in L” (such a best approximation necessari/J) exisrs) if and only if there exists a subinterual (a, /?) c IO. 1 I and a positilse integer M > r + 1 for which the following conditions hold (i) f”l,n.ll, is a Perfect spline of degree r with exactly) M ~ r -1 knots arzd I.f”““(s)l = I a. e. on [u,pI. i.e., there exists a = c,, < <, < ... < s’ II I I < 4, , = /I for which f*““(x) = E((l)I. <j 1 < My < Ti *
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