منابع مشابه
Algebraic values of analytic functions
Given an analytic function of one complex variable f , we investigate the arithmetic nature of the values of f at algebraic points. A typical question is whether f(α) is a transcendental number for each algebraic number α. Since there exist transcendental entire functions f such that f (t)(α) ∈ Q[α] for any t ≥ 0 and any algebraic number α, one needs to restrict the situation by adding hypothes...
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Analytic functions in tubes T B = R+iB in C, where B 1⁄2 R, that generalize the Hardy H spaces are studied. The associated function M¤ of Komatsu, which is de ̄ned with the aid of certain sequences of positive real numbers, is involved in the generalizing bound of the L norm. Fourier-Laplace and Cauchy integral representations are obtained for these functions. These representations can be used t...
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Let U, K, and C denote the open unit disc, the closed unit disc, and the unit circumference, respectively. Let A be the set of all complex-valued functions which are defined and continuous on K and analytic in U. The theorem proved in this paper states that if £ is a closed subset of C, of (Lebesgue) measure zero, and if <p is a continuous function defined on £, then there exists a function /£....
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6. M. M. Dragilev, "On compatibly regular bases in nonnuc!ear Kothe spaces," Mat. Zametki, 30, No. 6, 819-822 (1981). P. B. Djakov, "A short proof of the Crone and Robinson theorem on quasiequivalence of regular bases," Stud. Math., 53, No. 3, 269-271 (1975). V. P. Zakharyuta and V. P. Konkdakov, "on the weak equivalence of bases of Kothe spaces," Izv. SKNts, VSh, ~, 12-15 (1983). M. M. Dragile...
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For a holomorphic family of entire functions we study dependence of Picard exceptional values of these functions on the parameter. In 1926, Julia [5] studied singularities of implicit functions defined by equations f(z, w) = 0, where f is an entire function of two variables such that f(., w) 6≡ 0 for every w ∈ C. Among other things, he investigated the exceptional set P consisting of those w fo...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0330466-0