Abstract:
Sharp estimates of the circular indicator and type are obtained for nonzero entire functions of minimal growth that are divisible by an entire function F when the growth of the characteristics of the zero set of F is known, and the problem of representing a meromorphic function f on Cn as a quotient f=g/h is solved with best possible estimates on the circular indicators and the type of the entire functions g and h.
Citation:
B. N. Khabibullin, “The theorem on the least majorant and its applications. II. Entire and meromorphic functions of finite order”, Russian Acad. Sci. Izv. Math., 42:3 (1994), 479–500
\Bibitem{Kha93}
\by B.~N.~Khabibullin
\paper The theorem on the least majorant and its applications. II.~Entire and meromorphic functions of finite order
\jour Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 42
\issue 3
\pages 479--500
\mathnet{http://mi.mathnet.ru/eng/im869}
\crossref{https://doi.org/10.1070/IM1994v042n03ABEH001543}
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\zmath{https://zbmath.org/?q=an:0839.31007}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1994IzMat..42..479K}
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Linking options:
https://www.mathnet.ru/eng/im869
https://doi.org/10.1070/IM1994v042n03ABEH001543
https://www.mathnet.ru/eng/im/v57/i3/p70
This publication is cited in the following 6 articles:
E. G. Kudasheva, E. B. Menshikova, B. N. Khabibullin, “Dual construction and existence of (pluri)subharmonic minorant”, Ufa Math. J., 16:3 (2024), 65–73
B. N. Khabibullin, E. B. Menshikova, “Preorders on Subharmonic Functions and Measures with Applications to the Distribution of Zeros of Holomorphic Functions”, Lobachevskii J Math, 43:3 (2022), 587
B. N. Khabibullin, “Poisson–Jensen formulas and balayage of measures”, Eurasian Math. J., 12:4 (2021), 53–73
B. N. Khabibullin, A. P. Rozit, E. B. Khabibullina, “Order versions of the Hahn–Banach theorem and envelopes. II. Applications to the function theory”, J. Math. Sci. (N. Y.), 257:3 (2021), 366–409
B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. II”, Izv. Math., 65:5 (2001), 1017–1039
B. N. Khabibullin, “Paley problem for plurisubharmonic functions of finite lower order”, Sb. Math., 190:2 (1999), 309–321
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