On removal of periods of conjugate functions in multiply connected domains
type: Item
instance of: scholarly article
title: On removal of periods of conjugate functions in multiply connected domains
zbMATH Open document ID: 0592.30045
published in: Michigan Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: Let G be a domain in the complex plane bounded by n analytic Jordan curves \(\gamma_ 1,...,\gamma_ n\), \(\Gamma =\cup \gamma_ i\). The author proves that for each (n-1)-tuple of real numbers \(\Lambda_ 1,...,\Lambda_{n-1}\) and each positive Borel measure \(\mu\) on \(\Gamma\) satisfying \(\mu (\gamma_ i)>0\), \(i=1,...,n-1\) there exist real (real positive) \(\lambda_ 1,...,\lambda_{n-1}\) \((\lambda_ 1,...,\lambda_ n)\) such that the periods of the conjugate harmonic functions defined by the Poisson integral of the measure \({\tilde \mu}\): \({\tilde \mu}|_{\gamma_ i}\equiv \lambda_ i\mu |_{\gamma_ i}\) along \(\gamma_ 1,...,\gamma_{n-1}\) are equal to \(\Lambda_ 1,...,\Lambda_{n-1}.\) Some applications of this result (such as the existence in multiply connected domains of an analytic function in the Nevanlinna or the Hardy classes with prescribed modulus of boundary values) are given too.
Mathematics Subject Classification ID: 30E25
zbMATH DE Number: 3950963
zbMATH Keywords: boundary behaviour
zbMATH Keywords: Nevanlinna classes
zbMATH Keywords: periods of the conjugate harmonic functions
zbMATH Keywords: Poisson integral
zbMATH Keywords: multiply connected domains
author: Dmitry Khavinson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003081
OpenAlex ID: W2015403044
DOI: 10.1307/MMJ/1029003081
description: scientific article; zbMATH DE number 3950963