Effectiveness of similar sets of polynomials of two complex variables in polycylinders and in Faber regions
type: Item
instance of: scholarly article
title: Effectiveness of similar sets of polynomials of two complex variables in polycylinders and in Faber regions
zbMATH Open document ID: 0926.32001
DOI: 10.1155/S0161171298000817
author: K. A. M. Sayyed
author: M. S. Metwally
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1999-05-03T00:00:00Z
full work available at URL: https://eudml.org/doc/48292
review text: The authors consider a basic set \(\{P_{m,n} (z_1,z_2)\}\) of polynomials in the two complex variables \(z_1\) and \(z_2\), in two different regions. The first region is a polycylinder and the second region is a Faber region. When the set is a base then every polynomial of two complex variables is a linear combination of elements from this set. Hence \(z_1^m z_2^n\) will be uniquely represented as a finite sum of polynomials from the given set. This in turn makes it possible to represent every function of two complex variables, which is regular in a neighborhood of the origin, as an infinite sum of polynomials from the set. Definitions of Cannon functions and Cannon sum are given. The authors use functional analysis to prove few inequalities dealing with the bounds of the Cannon functions in both the polycylinder and the Faber regions.
Mathematics Subject Classification ID: 32A15
zbMATH DE Number: 1180650
zbMATH Keywords: simple sets
zbMATH Keywords: similar sets
zbMATH Keywords: Faber polynomials
zbMATH Keywords: polycylinder
zbMATH Keywords: Faber region
reviewed by: Hussain S. Nur
MaRDI profile type: Publication
OpenAlex ID: W1982919020
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description: scientific article; zbMATH DE number 1180650