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Izvestiya: Mathematics, 2011, Volume 75, Issue 1, Pages 1–27
DOI: https://doi.org/10.1070/IM2011v075n01ABEH002525 (Mi im4104) 		 
This article is cited in 23 scientific papers (total in 23 papers)

On the least possible type of entire functions of order $\rho\in(0,1)$ with positive zeros

G. G. Braichev, V. B. Sherstyukov

National Engineering Physics Institute "MEPhI"
English version PDF (369 kB) Citations (23)
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DOI: https://doi.org/10.1070/IM2011v075n01ABEH002525
Abstract: We find the greatest lower bound for the type of an entire function of order $\rho\in(0,1)$ whose sequence of zeros lies on one ray and has prescribed lower and upper $\rho$-densities. We make a thorough study of the dependence of this extremal quantity on $\rho$ and on properties of the distribution of zeros. The results are applied to an extremal problem on the radii of completeness of systems of exponentials.
Keywords: extremal problems, type of entire function, upper and lower densities of zeros, completeness of systems of exponentials.
Received: 06.04.2009
Revised: 31.08.2009
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2011, Volume 75, Issue 1, Pages 3–28
DOI: https://doi.org/10.4213/im4104
Bibliographic databases:
Document Type: Article
UDC: 517.547.22
MSC: 30D20, 30C15, 30D15, 46B15
Language: English
Original paper language: Russian
Citation: G. G. Braichev, V. B. Sherstyukov, “On the least possible type of entire functions of order $\rho\in(0,1)$ with positive zeros”, Izv. RAN. Ser. Mat., 75:1 (2011), 3–28; Izv. Math., 75:1 (2011), 1–27
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v75/i1/p3
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:1360
    Russian version PDF:237
    English version PDF:14
    References:75
    First page:35
     
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