Convolution of functions with free normalization
type: Item
instance of: scholarly article
zbMATH Open document ID: 0984.30009
author: Krzysztof Piejko
author: Jan Stankiewicz
published in: Demonstratio Mathematica
publication date: 2002-04-21T00:00:00Z
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C75
zbMATH DE Number: 1619025
zbMATH Keywords: convolution of functions
zbMATH Keywords: circular and angularly domains
MaRDI profile type: Publication
full work available at URL: dema-2001-0110
OpenAlex ID: W1484012920
DOI: 10.1515/DEMA-2001-0110
title: Convolution of functions with free normalization
review text: Let \(\mathcal H\) denote the class of functions which are regular in the unit disc \(\Delta =\{z: |z|<1\}\). For two functions \(f(z)=\sum _{n=0}^{\infty}a_nz^n\), \(g(z)=\sum _{n=0}^{\infty}b_nz^n\) in \(\mathcal H\), the convolution \(f*g\) is defined by \((f*g)(z)=\sum _{n=0}^{\infty}a_nb_nz^n\). Suppose that \(f(\Delta)\subset D_1\) and \(g(\Delta)\subset D_2\), where \(D_1\) and \(D_2\) are the given circular (disc, halfplane) or angularly domains. In this paper the authors determine \(D_3\) so that \((f*g)(\Delta)\subset D_3\). The authors motivate the paper with earlier known results.
reviewed by: Saminathan Ponnusamy
description: scientific article; zbMATH DE number 1619025