On a boundary analog of the Forelli theorem

Abstract

A boundary analog of the Forelli theorem for real-analytic functions is established, i.e., it is demonstrated that each real-analytic function f defined on the boundary of a bounded strictly convex domain D in the multidimensional complex space with the one-dimensional holomorphic extension property along families of complex lines passing through a boundary point and intersecting D admits a holomorphic extension to D as a function of many complex variables.