منابع مشابه
A Theorem on Entire Functions
Let G(k) = ∫ 1 0 g(x)e kxdx, g ∈ L1(0, 1). The main result of this paper is the following theorem. THEOREM 1. There exists g 6≡ 0, g ∈ C∞ 0 (0, 1), such that G(kj) = 0, kj < kj+1, limj→∞ kj =∞, limk→∞ |G(k)| does not exist, lim supk→+∞ |G(k)| = ∞. This g oscillates infinitely often in any interval [1− δ, 1], however small δ > 0 is. MSC: 30D15, 42A38, 42A63
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1963
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1963-0148916-5