Caltech/UCLA Joint Analysis Seminar

The complex plane acts on the space of entire function by translations, taking f(z) to f(z+w). B.Weiss showed in `97 that there exists a probability measure defined on the space of entire functions, which is invariant under this action. In this talk I will present optimal bounds on the minimal possible growth of functions in the support of such measures and discuss other growth-related problems inspired by this work. In particular, I will focus on the question of minimal possible growth-rate of frequently oscillating subharmonic functions. The talk is partly based on a joint work with L. Buhovsky, A. Logunov, and M. Sodin.