Approximation of subharmonic functions in the unit disk

zbMATH Open1180.31002arXiv0807.0856MaRDI QIDQ3634048

Igor Chyzhykov

Publication date: 23 June 2009

Abstract: Let u be a subharmonic function in D={|z|<1}. There exist an absolute constant C and an analytic function f in D such that int_D |u(z)-log|f(z)|| dm(z)<C where m denotes the plane Lebesgue measure. We also consider uniform approximation.

Full work available at URL: https://arxiv.org/abs/0807.0856

zbMATH Keywords

analytic functionapproximationsubharmonic functionsRiesz measure

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)

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