Abstract
We establish conditions for the representation of functions f(z) analytic in unbounded convex domains D and continuous in \(\bar D\) via series of the form \(\sum\nolimits_{n = 1}^\infty {P_n \left( z \right)} e^{\lambda _n z} \).
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References
E. K. Krutygolova, “On conditions of expandability of analytic functions in Dirichlet series in a half plane,” Ukr. Mat. Zh., 33, No. 1, 28–34 (1986).
A. F. Leont’ev, Series of Exponents [in Russian], Nauka, Moscow (1976).
E. K. Krutygolova and Yu. I. Mel’nik, “On conditions of convergence of Taylor-Dirichlet series in convex polygons,” Ukr. Mat. Zh., 46, No. 11, 1576–1580 (1994).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 812–817, June, 1998.
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Krutygolova, E.K. Representation of analytic functions by generalized series of exponents in unbounded convex domains. Ukr Math J 50, 922–928 (1998). https://doi.org/10.1007/BF02515225
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DOI: https://doi.org/10.1007/BF02515225