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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Suppose that f is a positive, nondecreasing, and integrable function in the interval (0, 1). Then, by Polya's theorem, all the zeros of the Laplace transform F(z) = integral(0)(1) e(zt)f(t) dt lie in the left-hand half-plane Re z less than or equal to 0. In this paper, we assume that the additional condition of logarithmic convexity of f in a left-hand neighborhood of the point I is satisfied. We obtain the form of the left curvilinear half-plane and also, under the condition f (+0) > 0, the form of the curvilinear strip containing all the zeros of F(z).