The Schwarz problem for polyanalytic functions
type: Item
instance of: scholarly article
title: The Schwarz problem for polyanalytic functions
zbMATH Open document ID: 1089.30040
DOI: 10.4171/ZAA/1244
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2006-03-10T00:00:00Z
review text: A function \(f\) on an open subset \(G\) of the complex plane is called polyanalytic of order \(n\) if there are functions \(f_0,f_1,...,f_{n-1}\) analytic in \(G\) such that \[ f(z)=\bar z^{n-1}f_{n-1}(z)+\cdots+\bar zf_1(z)+f_0(z). \] The authors use the polyanalytic Schwarz kernel to give higher order Cauchy--Schwarz--Pompeiu representations and solve the Schwarz problem for the Poisson equation, Bitsadze equation, and the inhomigeneous polyanalytic equation.
reviewed by: Vladimir V. Peller
Mathematics Subject Classification ID: 30E25
Mathematics Subject Classification ID: 30G20
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 35J40
zbMATH DE Number: 5011359
zbMATH Keywords: polyanalytic function
zbMATH Keywords: Schwarz kernel
author: Heinrich Begehr
author: Dieter Schmersau
MaRDI profile type: Publication
cites work: Q4846159
cites work: Q5200716
cites work: Q4676253
cites work: A hierarchy of integral operators
cites work: Q5515593
cites work: Q3844606
cites work: Q3281267
description: scientific article; zbMATH DE number 5011359