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 Mat. Sb. (N.S.), 1978, Volume 106(148), Number 3(7), Pages 386–408 (Mi msb2583)

The Fourier series method for entire and meromorphic functions of completely regular growth

A. A. Kondratyuk

Abstract: By using the Fourier series method, we generalize the Levin–Pfluger theory of entire functions of completely regular growth in two directions: a) We introduce classes of meromorphic functions of completely regular growth; b) the growth of a function is measured with respect to an arbitrary nondecreasing continuous function $\lambda(r)$ that satisfies $\lambda(2r)/\lambda(r)=O(1)$ as $r\to\infty$.
Bibliography: 20 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:1, 63–84

Bibliographic databases:

UDC: 517.535.4
MSC: 30D20, 30D30

Citation: A. A. Kondratyuk, “The Fourier series method for entire and meromorphic functions of completely regular growth”, Mat. Sb. (N.S.), 106(148):3(7) (1978), 386–408; Math. USSR-Sb., 35:1 (1979), 63–84

Citation in format AMSBIB
\Bibitem{Kon78}
\by A.~A.~Kondratyuk
\paper The Fourier series method for entire and meromorphic functions of completely regular growth
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 3(7)
\pages 386--408
\mathnet{http://mi.mathnet.ru/msb2583}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=505109}
\zmath{https://zbmath.org/?q=an:0426.30025|0392.30018}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 1
\pages 63--84
\crossref{https://doi.org/10.1070/SM1979v035n01ABEH001452}

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This publication is cited in the following articles:
1. A. A. Kondratyuk, “The Fourier series method for entire and meromorphic functions of completely regular growth. II”, Math. USSR-Sb., 41:1 (1982), 101–113
2. A. A. Kondratyuk, “On the method of spherical harmonics for subharmonic functions”, Math. USSR-Sb., 44:2 (1983), 133–148
3. Kondratyuk A., “Asymptotic-Behavior and the Number of Deficient Values of Entire-Functions with Completely Regular Growth”, no. 5, 1981, 11–13
4. A. A. Kondratyuk, “The Fourier series method for entire and meromorphic functions of completely regular growth. III”, Math. USSR-Sb., 48:2 (1984), 327–338
5. A. A. Kondratyuk, “Spherical harmonics and subharmonic functions”, Math. USSR-Sb., 53:1 (1986), 147–167
6. B. N. Khabibullin, “Balayage on a system of rays and entire functions of completely regular growth”, Math. USSR-Izv., 38:1 (1992), 179–197
7. K. G. Malyutin, “Fourier series and $\delta$-subharmonic functions of finite $\gamma$-type in a half-plane”, Sb. Math., 192:6 (2001), 843–861
8. Malyutin K. Sadik N., “Delta-Subharmonic Functions of Completely Regular Growth in the Half-Plane”, Dokl. Math., 64:2 (2001), 194–196
9. K. G. Malyutin, N. Sadik, “Representation of subharmonic functions in a half-plane”, Sb. Math., 198:12 (2007), 1747–1761
10. K. G. Malyutin, N. Sadyk, “Indikator delta-subgarmonicheskoi funktsii v poluploskosti”, Ufimsk. matem. zhurn., 3:4 (2011), 86–94
11. Ufa Math. J., 9:1 (2017), 123–136
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