A multidimensional version of Levin's Secular Constant Theorem and its applications

Abstract

We study holomorphic almost periodic functions on a tube domain with the spectrum in a cone. We extend to this case Levin's theorem on a connection between the Jessen function, secular constant, and the Phragmen-Lindelof indicator. Then we obtain a multidimensional version of Picard's theorem on exceptional values for our class.