2022/04/12 by Б. Н. Хабибуллин, Khabibullin, B. N.
Mathematics · #30D35 (Secondary) #31A05 (Primary) 30D15 #31A15 #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.2204.07461
openalex publication_date 2022/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider two balayage constructions on the complex plane \mathbb C with real axis \mathbb R for 0≤ b∈ \mathbb R. Let u\not≡ -∞ be a subharmonic function on \mathbb C of order ord[u]:=\limsupz→ ∞ \fracln max\1,u(z)\ln |z|≤ 1, U=u-v be the difference of subharmonic functions u and v\not≡ -∞ on \mathbb C with ord[v]≤ 1, i.e., δ-subharmonic function on \mathbb C of order ord[U]≤ 1. Then there is a δ-subharmonic function V\not≡ ±∞ on \mathbb C of order ord[V]≤ 1 such that V is harmonic on \ z ∈ \mathbb C\bigm| |\Re z|> b\ and U(z)≡ V(z) for all z∈ \ z ∈ \mathbb C\bigm| |\Re z|≤ b\∖ E where E⊂ \mathbb C is polar. If u is a subharmonic function of finite type under order 1, i.e., \limsupz→ ∞ (u(z))/(|z|) b\ such that\begincases u(z)≡ u\mathbb R(z)+ub(z) \text for all z∈ \mathbb R\bigcup \ z ∈ \mathbb C\bigm| |\Re z|≤ b\, u(z)≤ u\mathbb R(z) + ub(z) for each z∈ \mathbb C.\endcases At the same time, we trace special relationships between the various logarithmic characteristics of the Riesz mass and charge distributions of subharmonic and δ-subharmonic functions.