Abstract:
A sharp estimate is obtained for the infimum of the types of the entire functions f vanishing on a sequence Λ when the averaged counting function N(r,Λ) of the sequence has known type, and a best possible estimate is obtained for the types of the entire functions g and h in a representation of a meromorphic function f=g/h when the Nevanlinna characteristic T(r,f) has known type.
\Bibitem{Kha92}
\by B.~N.~Khabibullin
\paper On the type of entire and meromorphic functions
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 2
\pages 293--301
\mathnet{http://mi.mathnet.ru/eng/sm1087}
\crossref{https://doi.org/10.1070/SM1994v077n02ABEH003441}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1208212}
\zmath{https://zbmath.org/?q=an:0802.30023}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1994SbMat..77..293K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994NF83500003}
Linking options:
https://www.mathnet.ru/eng/sm1087
https://doi.org/10.1070/SM1994v077n02ABEH003441
https://www.mathnet.ru/eng/sm/v183/i11/p35
This publication is cited in the following 12 articles:
G. G. Braichev, “Zadacha Silvestra i mnozhestva edinstvennosti v klassakh tselykh funktsii”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy
matematicheskogo obrazovaniya, SMFN, 70, no. 1, Rossiiskii universitet druzhby narodov, M., 2024, 25–37
V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, J. Math. Sci. (N. Y.), 257:2 (2021), 246–272
G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, J. Math. Sci., 250:3 (2020), 419–453
G. G. Braichev, V. B. Sherstyukov, “On the Growth of Entire Functions with Discretely Measurable Zeros”, Math. Notes, 91:5 (2012), 630–644
G. G. Braichev, “The least type of an entire function of order ρ∈(0,1) having positive zeros with prescribed averaged densities”, Sb. Math., 203:7 (2012), 950–975
Braichev G.G., “Sharp Bounds for the Type of an Entire Function of Order Less Than 1 Whose Zeros Are Located on a Ray and Have Given Averaged Densities”, Dokl. Math., 86:1 (2012), 559–561
G. G. Braichev, V. B. Sherstyukov, “On the least possible type of entire functions of order ρ∈(0,1) with positive zeros”, Izv. Math., 75:1 (2011), 1–27
B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Sb. Math., 200:2 (2009), 283–312
Xiangdong Yang, “Incompleteness of exponential system in the weighted Banach space”, Journal of Approximation Theory, 153:1 (2008), 73
B. N. Khabibullin, “Zero sequences of holomorphic functions, representation
of meromorphic functions, and harmonic minorants”, Sb. Math., 198:2 (2007), 261–298
B. N. Khabibullin, “Criteria for (sub-)harmonicity and continuation of (sub-)harmonic functions”, Siberian Math. J., 44:4 (2003), 713–728
B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. II”, Izv. Math., 65:5 (2001), 1017–1039
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