Hartogs Extension For Generalized Tubes in CN

Abstract In 1906, Hartogs proved his famous holomorphic extension theorem for bounded domains in C n , however, not many results of this type exist for unbounded ones. One of such, already a classical result, is the Bochner tube theorem from 1938, and in this paper we consider its generalization to “widening tubes”. Namely, we establish a sufficient condition for holomorphic extension of CR functions from the boundary of a certain class of domains in C n , n ≥ 2 , which possess a growth condition at infinity.