منابع مشابه
Growth of Analytic Functions Along a Line.
Let J(z) be regular and of exponential type less than wr in the half plane x _ 0, and let I Xn } be an increasing positive sequence of unit density such that Xn+1 -n _ 5 > 0. It is known that under suitable restrictions and with a suitable measure of growth, the growth of the sequence tf(Xn) determines the growth off(x) for real x > 0. I have established the following results. Let e(x) be a con...
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In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.
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provided that {X„} is an increasing sequence of real numbers such that |X„ — n\ 0. This is the L2-analogue of the theorem, proved in different ways by Duffin and Schaeffer [6] and by B. Levin [8], that f(x) is bounded if {/(X„)} is bounded ; the cases of the two theorems when \n = n are due respectively to Plancherel and Pólya [il] and Cartwright [3]. The object of this pap...
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Let Ω be a domain in the N -dimensional real space, L be an elliptic differential operator, and (Tn) be a sequence whose members belong to a certain class of operators defined on the space of L-analytic functions on Ω. It is proved in this paper the existence of a dense linear manifold of L-analytic functions all of whose nonzero members have maximal cluster sets under the action of every Tn al...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1952
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.38.6.503