Abstract:
This paper presents a technique for constructing functions that are subharmonic in the complex plane, agree with a given subharmonic function u on a system S of rays with vertex at the origin, and are harmonic outside S. For a wide class of systems S, this technique permits one to obtain criteria for the complete regularity of growth of entire functions f on S in terms of the balayage of the distribution of zeros of f.
\Bibitem{Kha91}
\by B.~N.~Khabibullin
\paper Balayage on a system of rays and entire functions of completely regular growth
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 1
\pages 179--197
\mathnet{http://mi.mathnet.ru/eng/im1031}
\crossref{https://doi.org/10.1070/IM1992v038n01ABEH002192}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1130033}
\zmath{https://zbmath.org/?q=an:0744.30020|0725.30018}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..38..179K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992HG30700008}
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https://doi.org/10.1070/IM1992v038n01ABEH002192
https://www.mathnet.ru/eng/im/v55/i1/p184
This publication is cited in the following 5 articles:
B. N. Khabibullin, “Distributions of zeros and masses of entire and
subharmonic functions with restrictions on their growth along the strip”, Izv. Math., 88:1 (2024), 133–193
B. N. Khabibullin, A. V. Shmeleva, Z. F. Abdullina, “Balayage of measures and subharmonic functions to a system of rays. II. Balayages of finite genus and growth regularity on a single ray”, St. Petersburg Math. J., 32:1 (2021), 155–181
B. N. Khabibullin, A. V. Shmelyova, “Balayage of measures and subharmonic functions on a system of rays. I. Classic case”, St. Petersburg Math. J., 31:1 (2020), 117–156
B. N. Khabibullin, “On the Growth of Entire Functions of Exponential Type near a Straight Line”, Math. Notes, 70:4 (2001), 560–573
Vladimir Azarin, “Completely regular growth on a prescribed set of rays and the limit set of entire functions”, Complex Variables, Theory and Application: An International Journal, 37:1-4 (1998), 53
Citation in format AMSBIB
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