The Logarithm of the Modulus of an Entire Function as a Minorant for a Subharmonic Function outside a Small Exceptional Set

2020/04/22 by Б. Н. Хабибуллин, Khabibullin, Bulat N.
Mathematics · #26A12 (Secondary) #30D20 (Primary) 31A05 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2004.11723

openalex publication_date 2020/04/22 · openalex created_date 2020/05/01 · openalex updated_date 2026/07/28

Abstract

Let u\not≡ -∞ be a subharmonic function on the complex plane \mathbb C. In 2016, we obtained a result on the existence of an entire function f≠ 0 satisfying the estimate log|f|≤ \sf B_u on \mathbb C, where functions \sf B_u are integral averages of u for rapidly shrinking disks as it approaches infinity. We give another equivalent version of this result with log |f|≤ u outside a very small exceptional set if u is of finite order.

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