Epifanov, O. V. Preservation of functions not having completely regular growth by a convolution operator. (English) Zbl 0433.44009 Sib. Math. J. 20, 301-303 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document 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 Keywords:completely regular growth on rays; convolution operator PDF BibTeX XML Cite \textit{O. V. Epifanov}, Sib. Math. J. 20, 301--303 (1979; Zbl 0433.44009) Full Text: DOI References: [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 différentielles 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.