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Izvestiya: Mathematics, 2015, Volume 79, Issue 2, Pages 233–256
DOI: https://doi.org/10.1070/IM2015v079n02ABEH002741 (Mi im8064) 		 
This article is cited in 1 scientific paper (total in 1 paper)

An interpolation problem in the class of entire functions of zero order

O. A. Bozhenkoa, A. F. Grishinb, K. G. Malyutinba

a Sumy State University
b V. N. Karazin Kharkiv National University
English version PDF (339 kB) Citations (1)
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DOI: https://doi.org/10.1070/IM2015v079n02ABEH002741
Abstract: We obtain two criteria for the solubility of an ordinary free interpolation problem in the class of entire functions of (non-prescribed) finite type with respect to a zero proximate order $\rho(r)$. We impose only one natural restriction on $\rho(r)$ guaranteeing that the class considered consists not only of polynomials. One criterion is stated in terms of the measure determined by the interpolation nodes, and the other in terms of the canonical product generated by these nodes.
Keywords: zero proximate order, free interpolation, interpolation sequence, canonical product, Dirac measure, Nevanlinna counting function.
Received: 27.10.2012
Revised: 09.04.2014
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 2, Pages 21–44
DOI: https://doi.org/10.4213/im8064
Bibliographic databases:
Document Type: Article
UDC: 517.538.7
MSC: 30E05, 30D45
Language: English
Original paper language: Russian
Citation: O. A. Bozhenko, A. F. Grishin, K. G. Malyutin, “An interpolation problem in the class of entire functions of zero order”, Izv. RAN. Ser. Mat., 79:2 (2015), 21–44; Izv. Math., 79:2 (2015), 233–256
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v79/i2/p21
    • This publication is cited in the following 1 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:568
    Russian version PDF:184
    English version PDF:8
    References:72
    First page:50
     
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