Abstract
In this article, we give an overview of the most significant and important results on holomorphic extensions of functions along a fixed direction. We discuss the following geometric questions of multidimensional complex analysis:
• holomorphic extension along a bundle of complex straight line, the Forelly theorem;
• holomorphic continuation of functions with thin singularities along a fixed direction;
• holomorphic continuation of functions along a family of analytic curves.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 68, No. 1, Science — Technology — Education — Mathematics — Medicine, 2022.
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Sadullaev, A.S. Holomorphic Continuation of Functions along a Fixed Direction (Survey). J Math Sci 278, 675–690 (2024). https://doi.org/10.1007/s10958-024-06948-x
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DOI: https://doi.org/10.1007/s10958-024-06948-x