On a functional equation of Aczél and Chung
type: Item
instance of: scholarly article
title: On a functional equation of Aczél and Chung
zbMATH Open document ID: 0791.39008
DOI: 10.1007/BF01834001
author: John A. Baker
published in: Aequationes Mathematicae
publication date: 1994-07-13T00:00:00Z
full work available at URL: https://eudml.org/doc/137543
review text: The equation in the title, the locally integrable solutions of which have been determined in [Studia Sci. Math. Hungar. 17, 51-67 (1982; Zbl 0553.39005)] is \((*)\) \(\sum^ m_{j=0}F_ j(a_ jx+b_ jy)=\sum^ n_{k=1}G_ k(x)H_ k(y)\). The author solves the analogue of this equation for (Laurent Schwartz) distributions by first reducing it to the case where \(m=1\). This can be done because distributions are differentiable and, by applying \(b_ pD_ x-a_ pD_ y\) to \((*)\) \((D_ x\) and \(D_ y\) are the derivations with respect to \(x\) or \(y\), respectively), one gets a similar equation with (by 1) lower \(m\).
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 39B42
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 28A35
zbMATH DE Number: 493237
zbMATH Keywords: regular distributions
zbMATH Keywords: functional determinants
zbMATH Keywords: functional equations
zbMATH Keywords: differentiable functions
zbMATH Keywords: locally integrable solutions
MaRDI profile type: Publication
cites work: Q3346720
cites work: Q3671563
cites work: Equations of the form \(H(x\cdot y)=\sum_if_i(x)g_i(y)\)
cites work: Q3827009
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description: scientific article; zbMATH DE number 493237