Contents V.14 N.1 2023

  • CONTINUATION OF R−ANALYTIC FUNCTIONS ALONG PARALLEL LINES
    S.A. IMOMKULOV (pp. 120-124)
    10.30546/2219-1259.14.1.2023.120

    • Abstract.

    In this paper, we prove an analogue of the main Hartogs Lemma in the class of real-analytic functions: If a real-analytic function, defined in a cylindrical domain admits real analytic extension to a larger cylindrical domain along one-dimensional real lines in a fixed direction, then the extended function is a real-analytic in the larger domain except some singularity set. It is given a description of the singularity sets of such real analytic functions.

    Keywords:

    R-analytic function, separately-analytic function, P-measure, pluripolar set, pluriregular point, Hartogs Lemma, Forellis theorem.

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