Subharmonic almost periodic functions

Abstract

We prove that almost periodicity in the sense of distributions coincides with almost periodicity with respect to Stepanov's metric for the class of subharmonic functions in a strip {z belongs C : a < Imz < b}. We also prove that Fourier coefficients of these functions are continuous functions in Imz. Further, if the logarithm of a subharmonic almost periodic function is a subharmonic function, then it is almost periodic.