Necessary and sufficient conditions for Carlson’s theorem for entire functions
نویسندگان
چکیده
منابع مشابه
Necessary and Sufficient Conditions for Carlson's Theorem on Entire Functions.
A star on a Y (or a IT) wl'' be used throughout this paper to indicate that the index of the sum (or the product) is restricted to lie in A. Theorem 1 is an optimal extension of a celebrated theorem of Carlson which states that the only entire function/(z) satisfying (1.1) and (1.2) and such that/(ra) =0 for each positive integer ra is the null function f(z) =0. The necessity of condition (1.4)...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1974-0335804-1