Literature Cited
A. A. Gol'dberg and I. V. Ostrovskii, “On derivatives and primitives of entire functions of completely regular growth,” Teor. Funktsii, Funkts. Analiz Prilozhen.,18, 70–81 (1973).
L. Gruman, “The growth of entire solutions of differential equations of finite and infinite order,” Ann. Inst. Fourier,22, No. 1, 211–238 (1972).
B. Ya. Levin, Distributions of Zeros of Entire Functions, Amer. Math. Soc. (1972).
A. Martineau, “Equations différentielles d'ordre infini,” Bull. Soc. Math. France,95, No. 2, 109–154 (1967).
O. V. Epifanov, “A differential operator of infinite order in spaces of entire functions of exponential type,” Sib. Mat. Zh.,15, 318–331 (1974).
R. Edwards, Functional Analysis, Holt, Rinehart, and Winston, New York (1965).
D. Dickson, “Expansions in series of solutions of linear difference-differential and infinite order differential equations with constant coefficients,” Memor. Am. Math. Soc.,23, No. 1, 1–72 (1957).
V. S. Azarin, “On a characteristic property of functions of completely regular growth inside an angle,” Teor. Funktsii, Funkts. Analiz Prilozhen.,2, 55–67 (1966).
O. V. Epifanov, “On the problem of epimorphism of convolution in convex domains,” Mat. Zametki,16, No. 3, 415–422 (1974).
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Rostov State University, Rostov-on-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 20, No. 2, 420–422, March–April, 1979.
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Epifanov, O.V. Preservation of functions not having completely regular growth by a convolution operator. Sib Math J 20, 301–303 (1979). https://doi.org/10.1007/BF00970041
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DOI: https://doi.org/10.1007/BF00970041