Approximations by convolutions and antiderivativesстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Let g be a given function in L-1 = L-1(0, 1), and let B be one of the spaces L-p (0, 1), 1 <= p < infinity, or C-0[0, 1]. We prove that the set of all convolutions f * g, f E B, is dense in B if and only if g is nontrivial in an arbitrary right neighborhood of zero. Under an additional restriction on g, we prove the equivalence in B of the systems fn * g and If,,,, where fn is an element of L-1, n is an element of N, and If = f * 1 is the antiderivative of f. As a consequence, we obtain criteria for the completeness and basis property in B of subsystems of antiderivatives of g.