Abstract:
In this paper the following result is proved:
Theorem.Let λi,i=1,…,n, be given such that λi⩾0 and ∑λi=1. Then any entire function f(z) of finite order ρ can be presented as a product of factors fi(z) such that
ln|fi(z)|=λiln|f(z)|+o(|z|ρ),i=1,…,n,
as z→∞,z outside a C0-set. Bibliography: 3 titles.
Citation:
V. S. Azarin, “On the decomposition of an entire function of finite order into factors having given growth”, Math. USSR-Sb., 19:2 (1973), 225–226
\Bibitem{Aza73}
\by V.~S.~Azarin
\paper On the decomposition of an entire function of finite order into factors having given growth
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 2
\pages 225--226
\mathnet{http://mi.mathnet.ru/eng/sm3008}
\crossref{https://doi.org/10.1070/SM1973v019n02ABEH001747}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=324031}
\zmath{https://zbmath.org/?q=an:0253.30018}
Linking options:
https://www.mathnet.ru/eng/sm3008
https://doi.org/10.1070/SM1973v019n02ABEH001747
https://www.mathnet.ru/eng/sm/v132/i2/p229
This publication is cited in the following 9 articles:
R. G. Pismennyi, “O razlozhenii tseloi funktsii konechnogo poryadka na ekvivalentnye mnozhiteli”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 9:1 (2009), 19–30
E. G. Kudasheva, B. N. Khabibullin, “Variation of subharmonic function under transformation of its Riesz measure”, Zhurn. matem. fiz., anal., geom., 3:1 (2007), 61–94
R. S. Yulmukhametov, “Solution of the Ehrenpreis factorization problem”, Sb. Math., 190:4 (1999), 597–629
I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. III: Ample submodules”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 165–188
A. B. Shishkin, “Spectral synthesis for an operator generated by multiplication by a power of the independent variable”, Math. USSR-Sb., 73:1 (1992), 211–229
B. N. Khabibullin, “Comparison of subharmonic functions by means of their associated measures”, Math. USSR-Sb., 53:2 (1986), 523–539
V. A. Tkachenko, “Spectral theory in spaces of analytic functionals for operators generated by multiplication by the independent variable”, Math. USSR-Sb., 40:3 (1981), 387–427
V. A. Tkachenko, “On operators commuting with generalized differentiation in spaces of analytic functionals with given indicator of growth”, Math. USSR-Sb., 31:3 (1977), 389–407
Citation in format AMSBIB
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