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Preservation of the completely regular growth by a differential operator of infinite order. (English. Russian original) Zbl 0695.47043
Translation from Teor. Funkts., Funkts. Anal. Prilozh. 47, 85–89 (1987; Zbl 0662.47024).
MSC:
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
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[1] B. Ya. Levin (B. Ja. Levin), Distribution of Zeros of Entire Functions, Am. Math. Soc., Providence (1964).
[2] I. V. Ostrovskii, ?Operators preserving the complete regular growth,? J. Sov. Math.,22, No. 1 (1983).
[3] H. Muggli, ?Differentialgleichungen unendlich hoher Ordnung mit konstanten Koeffizienten,? Comment. Math. Helv.,11, 151?179 (1938). · JFM 64.0426.02 · doi:10.1007/BF01199696
[4] Yu. F. Korobeinik, ?On certain characteristic properties of differential operators of infinite order,? Izv. Akad. Nauk SSSR, Ser. Mat.,30, No. 5, 933?1016 (1966).
[5] A. A. Gol’dberg and I. V. Ostrovskii, ?The derivatives and primitives of entire functions of completely regular growth,? Teor. Funktsii Funktsional. Anal. Prilozhen. (Kharkov), No. 18, 70?81 (1973).
[6] O. V. Epifanov, ?Preservation by the operator of convolution of the not entirely regular growth of functions,? Sib. Mat. Zh.,20, No. 2, 420?422 (1979). · Zbl 0433.44009 · doi:10.1007/BF00970041
[7] V. S. Azarin, ?On the rays of completely regular growth of an entire function,? Mat. Sb.,79 (121), 463?476 (1969). · Zbl 0197.35502
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