On some sets sufficient for holomorphic continuation of functions with generalized boundary Morera property

Abstract

This article considers continuous functions defined on the boundary of a bounded domain $D$ in $\mathbb C^n$, $n>1$, and having a generalized boundary Morera property. The question of the existence of a holomorphic continuation of such functions into the domain $D$ for some sufficient sets $\Gamma$ of complex lines intersecting the germ of the generating manifold lying inside the domain is investigated.