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Ufa Mathematical Journal, 2017, Volume 9, Issue 4, Pages 22–34
DOI: https://doi.org/10.13108/2017-9-4-22
(Mi ufa400)
 

This article is cited in 3 scientific papers (total in 3 papers)

Pavlov–Korevaar–Dixon interpolation problem with majorant in convergence class

R. A. Gaisin

Bashkir State University, Zaki Validi str. 32, 450077, Ufa, Russia
References:
Abstract: We study an interpolation problem in the class of entire functions of exponential type determined by some majorant in a convergence class (non-quasianalytic majorant). In a smaller class, when the majorant possessed a concavity property, similar problem was studied by B. Berndtsson with the nodes at some subsequence of natural numbers. He obtained a solvability criterion for this interpolation problem. At that, he applied first the Hörmander method for solving a $\overline{\partial}$-problem. In works by A.I. Pavlov, J. Korevaar and M. Dixon, interpolation sequences in the Berndtsson sense were applied successfully in a series of problems in the complex analysis. At that, there was found a relation with approximative properties of the system of powers $\{z^{p_n}\}$ and with the well known Polya and Macintyre problems.
In this paper we establish the criterion of the interpolation property in a more general sense for an arbitrary sequence of real numbers. In the proof of the main theorem we employ a modification of the Berndtsson method.
Keywords: interpolation sequence, entire function, convergence class.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-01661_а
The work is supported by RFBR (grant no. 15-01-01661).
Received: 14.09.2017
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 30E05
Language: English
Original paper language: Russian
Citation: R. A. Gaisin, “Pavlov–Korevaar–Dixon interpolation problem with majorant in convergence class”, Ufa Math. J., 9:4 (2017), 22–34
Citation in format AMSBIB
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\by R.~A.~Gaisin
\paper Pavlov--Korevaar--Dixon interpolation problem with majorant in convergence class
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 4
\pages 22--34
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  • https://doi.org/10.13108/2017-9-4-22
  • https://www.mathnet.ru/eng/ufa/v9/i4/p22
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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