Holomorphic continuation of functions along a fixed direction (survey)

A. S. Sadullaev

Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 68 (2022) no. 1, pp. 127-143.

Résumé

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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