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Preservation of functions not having completely regular growth by a convolution operator. (English) Zbl 0433.44009

MSC:
44A35 Convolution as an integral transform
47Gxx Integral, integro-differential, and pseudodifferential operators
45P05 Integral operators
30D15 Special classes of entire functions of one complex variable and growth estimates
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[1] 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).
[2] L. Gruman, ?The growth of entire solutions of differential equations of finite and infinite order,? Ann. Inst. Fourier,22, No. 1, 211-238 (1972). · Zbl 0221.35005
[3] B. Ya. Levin, Distributions of Zeros of Entire Functions, Amer. Math. Soc. (1972).
[4] A. Martineau, ?Equations diffĂ©rentielles d’ordre infini,? Bull. Soc. Math. France,95, No. 2, 109-154 (1967). · Zbl 0167.44202
[5] O. V. Epifanov, ?A differential operator of infinite order in spaces of entire functions of exponential type,? Sib. Mat. Zh.,15, 318-331 (1974). · Zbl 0309.47032
[6] R. Edwards, Functional Analysis, Holt, Rinehart, and Winston, New York (1965).
[7] 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). · Zbl 0079.11305
[8] 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).
[9] O. V. Epifanov, ?On the problem of epimorphism of convolution in convex domains,? Mat. Zametki,16, No. 3, 415-422 (1974). · Zbl 0314.47023
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