Article

    Ufa Mathematical Journal
    Volume 9, Number 4, pp. 22-34

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


    Gaisin R.A.

    DOI:10.13108/2017-9-4-22

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    We study interpolation problem in the class of entire functions of exponential type determined by some majorant from convergence class. Analogous problem in subclass in which majorant carried concavity property was considered by B. Berndtsson but nodes were in the points of some subsequence of natural numbers. He obtained criterion of solvability of this interpolation problem. He was first who used Hermander's $\overline{\partial}$-problem solving method. In the works of A.I. Pavlov, J. Korevaar and M. Dixon interpolation sequences in the sense of B. Berndtsson were succesfully used in series of problems of complex analysis. In addition was found some relation with approximative properties of the system of powers $\{z^{p_n}\}$ and with well known Polya and Macintyre problems. In this paper criterion of interpolationality in more general sense is established for arbitrary sequence of real numbers. In the proof of the main theorem modified method of B. Berndtsson is used.