Abstract:
The paper is devoted to the theory of extremal problems in classes of entire functions with constraints on the growth and distribution of zeros and is associated with problems of completeness of exponential systems in the complex domain. The question of finding the exact lower bound for types of all entire functions of order ρ∈(0,1) whose zeros lie on the ray and have prescribed upper ρ-density and ρ-step is discussed. It is shown that the infimum is attained in this problem, and a detailed construction of the extremal function is given. This result gives a complete solution of the extremal problem and generalizes preceding result of A. Yu. Popov.
Key words:
type of an entire function, upper density and step of sequence of zeros, extremal problemю.
Bibliographic databases:
Document Type:
Article
UDC:517.547.2
Language: Russian
Citation:
O. V. Sherstyukova, “On the least type of entire functions of order ρ∈(0,1) with positive zeros”, Izv. Saratov Univ. Math. Mech. Inform., 15:4 (2015), 433–441
\Bibitem{She15}
\by O.~V.~Sherstyukova
\paper On the least type of entire functions of order $\rho\in(0,1)$ with positive zeros
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 4
\pages 433--441
\mathnet{http://mi.mathnet.ru/isu611}
\crossref{https://doi.org/10.18500/1816-9791-2015-15-4-433-441}
\elib{https://elibrary.ru/item.asp?id=25360659}
Linking options:
https://www.mathnet.ru/eng/isu611
https://www.mathnet.ru/eng/isu/v15/i4/p433
This publication is cited in the following 3 articles:
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
O. V. Sherstyukova, “The problem on the minimal type of entire functions of order ρ∈(0,1) with positive zeroes of prescribed densities and step”, Ufa Math. J., 7:4 (2015), 140–148
Citation in format AMSBIB
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