Separation principles and Riemann-Hilbert problems
type: Item
instance of: scholarly article
title: Separation principles and Riemann-Hilbert problems
zbMATH Open document ID: 1027.30061
DOI: 10.1007/BF03321015
author: G. Semmler
author: E. Wegert
published in: Computational Methods and Function Theory
publication date: 2003-10-22T00:00:00Z
review text: Let \(w_\pm\) be the holomorphic functions on the unit disk \(D\subset \mathbb{C}\) and let \(M_t=\{x+if(t,x)\},\;x\in R,\;t\in\partial D\) where \(f(t,x)\) is real-valued. For a given subset \(A\) in the Hardy space \(H^1\) denote by \(A_+=\{w_+\in A, v_+(t)\geq f(t,u_+(t))\;a.e.\;on\;\partial D\}\) and \(A_-=\{w_-\in A, v_-(t)\geq f(t,u_-(t))\;a.e.\;on\;\partial D\}\) the sets of upper \(w_+=u_++iv_+\) and lower \(w_-=u_-+iv_-\) functions. The author compares the values of upper and lower functions in inner points of \(D\). In particular are studied the conditions on the class \(A\) and separating curve \(M_t\) which guarantee that the values \(w_+ (0)\) of upper functions lie ''above'' the values \(w_- (0)\) of lower functions.
Mathematics Subject Classification ID: 30E25
Mathematics Subject Classification ID: 30C75
zbMATH DE Number: 1995500
zbMATH Keywords: holomorphic functions
zbMATH Keywords: normal family
zbMATH Keywords: separation principle
zbMATH Keywords: Riemann-Hilbert problem
reviewed by: N. Karapetiants
MaRDI profile type: Publication
cites work: Q5618011
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cites work: Nonlinear Riemann—Hilbert problems with Lipschitz continuous boundary condition
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description: scientific article; zbMATH DE number 1995500