Asymptotic behavior of subfunctions of the stationary Schrodinger operator

TL;DR

This paper investigates the asymptotic behavior of subfunctions related to the stationary Schrödinger operator, extending classical results on analytic and subharmonic functions to this context.

Contribution

It establishes analogs of classical theorems like Phragmen-Lindelof, Blaschke, Carleman, and Hayman-Azarin for subharmonic functions associated with the Schrödinger operator.

Findings

Derived growth rate estimates for subfunctions

Extended classical theorems to Schrödinger-related subharmonic functions

Analyzed asymptotic behavior in multi-dimensional cones

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.