The growth of subharmonic functions along the imaginary axis

2019/11/18 by A. Е. Egorova, Egorova, Anna E., Б. Н. Хабибуллин +1
Mathematics · #30B60 #30D20 #31A05 #32A60 #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1911.07890

openalex publication_date 2019/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let u\not≡ -∞ and M\not≡ -∞ are two subharmonic functions in the complex plane \mathbb C with the Riesz measures ν_u and μ_M such that u(z)≤ O(|z|) and M(z)≤ O(|z|) as z→ ∞. If the growth of a function M in some sense exceeds the growth of a function u on some straight line, then we can expect measure μ_M to dominate measure ν_u in some sense. We give quantitative forms of such dominance. The main results are illustrated by a new uniqueness theorem for entire functions of exponential type.

Related

• Growth Estimates for a Class of Subharmonic Functions in a Half Plane
• Growth of Subharmonic Functions
• Self-improving estimates of growth of subharmonic and analytic functions
• Asymptotic Behaviour for a Class of Subharmonic Functions in a Half Space
• Some results on Complex m-subharmonic classes