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 Mat. Sb. (N.S.), 1980, Volume 113(155), Number 1(9), Pages 118–132 (Mi msb2781)

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

A. A. Kondratyuk

Abstract: The Fourier series method is used to obtain an integral criterion for an entire function to be of completely regular growth.
It is shown that when the pair $(Z,W)$ of sequences $Z$ of zeros and $W$ of poles of a meromorphic function $f$ has an angular density, the function belongs to the class $\Lambda^0$ of meromorphic functions of completely regular growth introduced in Part I of this paper, and the asymptotic properties of this function are studied. A function $f\in\Lambda^0$ for which $(Z,W)$ does not have an angular density is constructed; examples of $[\varkappa,\rho]$-trigonometrically convex functions are presented.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 41:1, 101–113

Bibliographic databases:

UDC: 517.535.4
MSC: 30D15, 30D35

Citation: A. A. Kondratyuk, “The Fourier series method for entire and meromorphic functions of completely regular growth. II”, Mat. Sb. (N.S.), 113(155):1(9) (1980), 118–132; Math. USSR-Sb., 41:1 (1982), 101–113

Citation in format AMSBIB
\Bibitem{Kon80} \by A.~A.~Kondratyuk \paper The Fourier series method for entire and meromorphic functions of completely regular growth.~II \jour Mat. Sb. (N.S.) \yr 1980 \vol 113(155) \issue 1(9) \pages 118--132 \mathnet{http://mi.mathnet.ru/msb2781} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=590541} \zmath{https://zbmath.org/?q=an:0441.30036} \transl \jour Math. USSR-Sb. \yr 1982 \vol 41 \issue 1 \pages 101--113 \crossref{https://doi.org/10.1070/SM1982v041n01ABEH002223} 

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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. III”, Math. USSR-Sb., 48:2 (1984), 327–338
2. A. A. Kondratyuk, “Spherical harmonics and subharmonic functions”, Math. USSR-Sb., 53:1 (1986), 147–167
3. K. G. Malyutin, “Fourier series and $\delta$-subharmonic functions of finite $\gamma$-type in a half-plane”, Sb. Math., 192:6 (2001), 843–861
4. Malyutin K., Sadik N., “Delta-Subharmonic Functions of Completely Regular Growth in the Half-Plane”, Dokl. Math., 64:2 (2001), 194–196
5. K. G. Malyutin, N. Sadik, “Representation of subharmonic functions in a half-plane”, Sb. Math., 198:12 (2007), 1747–1761
6. K. G. Malyutin, N. Sadyk, “Indikator delta-subgarmonicheskoi funktsii v poluploskosti”, Ufimsk. matem. zhurn., 3:4 (2011), 86–94
7. Ufa Math. J., 9:1 (2017), 123–136
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