Héctor Cuenya

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In this paper we give sufficient conditions over the differentiability of a function to assure existence of the best local approximant in L p-spaces, 0 < p ≤ ∞. These conditions are weaker than those given in previous papers. For p = 2 we show that, in a certain way, they are also necessary. In addition, we characterize the best local approximant.
Given f E L2(lR n), E > 0 and x E IR n we consider P(t) to be the polynomial of best approximation to f in the L2-norm by elements of IIm over the set x + EC, where C denote a suitable parallelepiped. Let T;'f(x) be the Qth-coefficient of P when it has been developed in the base {t"'/Q!}. In this paper we show that the operator T;' is a composition of a(More)
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