CONTINUATION OF R−ANALYTIC FUNCTIONS ALONG PARALLEL LINESS.A. IMOMKULOV (pp. 120-124)
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.