Geodesic
Complete regularity of growth for some classes of entire functions of exponential type represented by Р’orel integrals and power series
Izvestiya. Mathematics, Tome 27 (1986) no. 3, pp. 431-450 Cet article a éte moissonné depuis la source Math-Net.Ru

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New tests are obtained for the regularity of growth of entire functions of exponential type that are represented as power series $F(z)=\sum_{n=0}^\infty\frac{a_n}{n!}z^n$ and Borel (Laplace) integrals $F(z)=\int_Lf(\tau)e^{z\tau}\,d\tau$. Bibliography: 16 titles. 
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     title = {Complete regularity of growth for some classes of entire functions of exponential type represented by {{\CYRR}{\textquoteright}orel} integrals and power series},
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N. V. Govorov; N. M. Chernykh. Complete regularity of growth for some classes of entire functions of exponential type represented by Р’orel integrals and power series. Izvestiya. Mathematics, Tome 27 (1986) no. 3, pp. 431-450. http://geodesic.mathdoc.fr/item/IM2_1986_27_3_a1/

[1] Govorov N. V., Chernykh N. M., “O priznakakh polnoi regulyarnosti rosta nekotorykh klassov tselykh funktsii eksponentsialnogo tipa, predstavlennykh integralami Borelya, ryadami Nyutona, Dirikhle i stepennymi ryadami”, Dokl. AN SSSR, 249:6 (1979), 1295–1299 | MR | Zbl

[2] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956

[3] Lindelöf E., “Sur la determination de la croissance des fonctions entieres définies par un développement de Taylor”, Bull. Sci. math. (2), 27 (1903), 213–226 | Zbl

[4] Azarin V. S., “Ob odnom kharakteristicheskom svoistve funktsii vpolne regulyarnogo rosta vnutri ugla”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, vyp. 2, Kharkov, 1966 | MR | Zbl

[5] Logvinenko V. N., “Postroenie tseloi funktsii s zadannym indikatorom pri zadannom utochnennom poryadke”, Funkts. analiz i ego prilozh., 6:4 (1972), 87–88 | MR | Zbl

[6] Chernolyas V. I., “O tselykh funktsiyakh obobschennogo vpolne regulyarnogo rosta proizvolnogo verkhnego i nizhnego poryadka”, Dokl. AN SSSR, 234:4 (1977), 772–775 | MR | Zbl

[7] Markushevich A. I., Teoriya analiticheskikh funktsii, 2-e izd., Nauka, M., 1967

[8] Biberbakh L., Analiticheskoe prodolzhenie, Nauka, M., 1967 | MR

[9] Markushevich A. I., Izbrannye glavy teorii analiticheskikh funktsii, Nauka, M., 1976 | MR | Zbl

[10] Govorov N. V., Zhurbitskaya V. V., “Ob odnom priznake polnoi regulyarnosti rosta funktsii, analiticheskikh v ugle”, Lit. matem. sb., 17:3 (1977), 133

[11] Govorov N. V., Chernykh N. M., “O polnoi regulyarnosti rosta preobrazovaniya Borelya s konechnym chislom osobykh tochek analiticheskogo prodolzheniya assotsiirovannoi funktsii”, Izv. AN SSSR. Ser. matem., 42:5 (1978), 965–971 | MR | Zbl

[12] Macintyre A. T., “Laplase transformation and integral functions”, Proc. Lond. Math. Soc., 45:2 (1938), 1–20 | MR | Zbl

[13] Gakhov F. D., Kraevye zadachi, 3-e izd. pererab. i dop., Nauka, M., 1977 | MR

[14] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR | Zbl

[15] Khavin V. P., “O vydelenii osobennostei analiticheskikh funktsii”, Dokl. AN SSSR, 121:2 (1958), 239–242 | Zbl

[16] Chernykh N. M., Priznak polnoi regulyarnosti rosta analiticheskikh v ugle funktsii s trigonometricheskim indikatorom, rukopis predstavlena Kuban. un-tom. Dep. v VINITI 8 apr. 1980, No 1346-80, Krasnodar, 1980