Geodesic
Pavlov–Korevaar–Dixon interpolation problem with majorant in convergence class
Ufa mathematical journal, Tome 9 (2017) no. 4, pp. 22-34 Cet article a éte moissonné depuis la source Math-Net.Ru

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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: entire function
Mots-clés : interpolation sequence, convergence class. 
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     title = {Pavlov{\textendash}Korevaar{\textendash}Dixon interpolation problem with majorant in convergence class},
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R. A. Gaisin. Pavlov–Korevaar–Dixon interpolation problem with majorant in convergence class. Ufa mathematical journal, Tome 9 (2017) no. 4, pp. 22-34. http://geodesic.mathdoc.fr/item/UFA_2017_9_4_a2/

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