Asymptotic behavior of subfunctions of the stationary Schrodinger operator

Abstract

Subharmonic functions associated with the stationary Schrodinger operator are its weak subsolutions under appropriate assumptions on the potential of the operator. We prove for these functions analogs of several classical results on analytic and subharmonic functions, such as the Phragmen-Lindelof theorem with the precise growth rate, the Blaschke theorem on bounded analytic functions, the Carleman formula, the Hayman-Azarin theorem on asymptotic behavior of special subharmonic functions in many-dimensional cones.