Abstract:
The following questions are considered. A connection is found in general form between the rate of growth of the maximum modulus of an entire function and the rate of decrease of the moduli of its Maclaurin coefficients. Moreover, a study is made of the distribution of zeros of the successive derivatives of zero-order entire functions and entire functions of exponential type.
\Bibitem{Osk93}
\by V.~A.~Oskolkov
\paper On some questions in the~theory of entire functions
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 78
\issue 1
\pages 113--129
\mathnet{http://mi.mathnet.ru/eng/sm959}
\crossref{https://doi.org/10.1070/SM1994v078n01ABEH003461}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1211369}
\zmath{https://zbmath.org/?q=an:0810.30018}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994NR97600007}
Linking options:
https://www.mathnet.ru/eng/sm959
https://doi.org/10.1070/SM1994v078n01ABEH003461
https://www.mathnet.ru/eng/sm/v184/i1/p129
This publication is cited in the following 9 articles:
M. V. Kabanko, K. G. Malyutin, B. N. Khabibullin, “Ob utochnennoi funktsii rosta otnositelno modelnoi”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 230, VINITI RAN, M., 2023, 56–74
G. G. Braichev, “Joint estimates for zeros and Taylor coefficients of entire function”, Ufa Math. J., 13:1 (2021), 31–45
G. G. Braichev, “Ob odnoi probleme Adamara i sglazhivanii vypuklykh funktsii”, Vladikavk. matem. zhurn., 7:3 (2005), 11–25
Kozko A., “Asymptotics of the Spectrum of the Differential Operator -Y"+Q(X)Y with a Boundary Condition at Zero and with Rapidly Growing Potential”, Differ. Equ., 41:5 (2005), 636–648
A. Yu. Popov, “On the completeness of sparse subsequences of systems of functions of the form f(n)(λnz)”, Izv. Math., 68:5 (2004), 1025–1049
A. Yu. Popov, “Bounds for convergence and uniqueness in Abel–Goncharov interpolation
problems”, Sb. Math., 193:2 (2002), 247–277
S. A. Shkarin, “On effective linearly ordered sets of comparison functions”, Math. Notes, 67:4 (2000), 534–540
Yu. F. Korobeinik, “A relationship between the maximum modulus and Taylor coefficients of entire functions of several complex variables”, Math. Notes, 62:2 (1997), 198–215
V. A. Oskolkov, L. I. Kalinichenko, “Growth of entire functions represented by Dirichlet series”, Sb. Math., 187:10 (1996), 1545–1560
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