Wilson's functional equation on \(\mathbb{C}\)
type: Item
instance of: scholarly article
title: Wilson's functional equation on \(\mathbb{C}\)
zbMATH Open document ID: 0869.39007
DOI: 10.1007/BF02215967
author: Henrik Stetkær
published in: Aequationes Mathematicae
publication date: 1997-03-06T00:00:00Z
full work available at URL: https://eudml.org/doc/137679
review text: The author obtains the solutions of the Wilson functional equation \[ \frac{1}{N} \sum^{N-1}_{n=0} f(x+w^ny)= f(x)g(y), \qquad x,y\in\mathbb{C}, \] by relating its solutions to two other equations \[ \frac{1}{N} \sum^{N-1}_{n=0} f(x+w^ny) w^{nr}= g(x)f(y), \qquad x,y\in\mathbb{C}, \] and \[ \frac{1}{N} \sum^{N-1}_{n=0} g(x+w^n y)=g(x)g(y), \qquad x,y\in\mathbb{C}, \] where \(w^N=1\) and \(w^m\neq 1\) for \(m=1,2,\dots, N-1\), \(r=0,1,\dots, N-1\).
reviewed by: Pl. Kannappan
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 988014
zbMATH Keywords: closed form solution
zbMATH Keywords: Wilson functional equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 988014