Poisson-Jensen Formulas and Balayage of Measures

2020/04/27 by Б. Н. Хабибуллин, Khabibullin, Bulat N.
Mathematics · #26A51 (Secondary) #31A05 (Primary) 31B15 #31A15 #31B05 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2005.00408

openalex publication_date 2020/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our main results are certain developments of the classical Poisson--Jensen formula for subharmonic functions. The basis of the classical Poisson--Jensen formula is the natural duality between harmonic measures and Green's functions. Our generalizations use some duality between the balayage of measures and and their potentials.

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