On the relation between the growth and the Taylor coefficients of entire solutions to the higher-dimensional Cauchy--Riemann system in \(\mathbb R^{n+1}\)
type: Item
instance of: scholarly article
title: On the relation between the growth and the Taylor coefficients of entire solutions to the higher-dimensional Cauchy--Riemann system in \(\mathbb R^{n+1}\)
zbMATH Open document ID: 1108.30041
author: D. Constales
author: R. De Almeida
author: R. S. Kraußhar
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-01-09T00:00:00Z
review text: The authors establish an interesting relation between the coefficients of the Taylor expansion of entire holomorphic functions in Clifford analysis and the growth order of the maximum modulus which is known from classical function theory. This allows to determine the growth order without knowing the maximum modulus. Examples of any finite order are given, the generalized trigonometric functions have the order 1.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 30D15
zbMATH DE Number: 5083311
zbMATH Keywords: Clifford analysis
zbMATH Keywords: growth orders
zbMATH Keywords: entire holomorphic functions
zbMATH Keywords: maximum modulus
zbMATH Keywords: generalized trigonometric functions
reviewed by: Klaus Habetha
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.04.055
OpenAlex ID: W2089182852
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DOI: 10.1016/J.JMAA.2006.04.055
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description: scientific article; zbMATH DE number 5083311