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Extensions of Analytic and Pluriharmonic Functions in Given Directions by the Chirka Method: a Survey

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In this paper, we provide a survey of results on analytic and plurisubharmonic extensions of functions that have a thin set of singularities along a fixed direction. We show the advantages of using the pluripotential theory and the Jacobi–Hartogs series for description of the singular set of such functions.

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Authors and Affiliations

  1. National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan

    A. Sadullaev

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  1. A. Sadullaev
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Correspondence to A. Sadullaev.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 65, No. 1, Contemporary Problems in Mathematics and Physics, 2019.

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Sadullaev, A. Extensions of Analytic and Pluriharmonic Functions in Given Directions by the Chirka Method: a Survey. J Math Sci 265, 79–89 (2022). https://doi.org/10.1007/s10958-022-06046-w

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