Generalized sine equations. I
type: Item
instance of: scholarly article
title: Generalized sine equations. I
zbMATH Open document ID: 0811.39003
DOI: 10.1007/BF01832984
author: Pavlos Sinopoulos
published in: Aequationes Mathematicae
publication date: 1994-12-07T00:00:00Z
full work available at URL: https://eudml.org/doc/137606
review text: This is the first of a sequence of papers on functional equations of the form \[ f_ 1 (x+y )f_ 2 (x-y) = \sum^ n_{k=0} g_ k (x)h_ k (y). \] The present paper deals with the cases (i) \(n=1\), \(h_ 1 = id\), (ii) \(n = 2\), \(h_ k = h^ k\) \((k=0,1,2)\) with additive or multiplicative \(h\), and (iii) \(n\) arbitrary, one of the \(g_ k\)'s and one of the \(h_ k\)'s is identically 1 (both the \(\{g_ k\}\) and the \(\{h_ k\}\) are supposed to be linearly independent). In (i) and (iii) the values of the functions lie in an algebraically closed field of characteristic 0, while their domain is a divisible abelian group or an abelian group divisible by 2, respectively. In (ii) the range is \(\mathbb{C}\), the domain is \(\mathbb{R}\).
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 699776
zbMATH Keywords: generalized sine equations
zbMATH Keywords: Wilson functional equations
zbMATH Keywords: algebraically closed field
zbMATH Keywords: general solution
zbMATH Keywords: abelian group
zbMATH Keywords: functional equation
MaRDI profile type: Publication
cites work: Q5514010
cites work: The state of the second part of Hilbert’s fifth problem
cites work: On the functional equation \(f(x)g(y) = \prod\limits_{i=1}^n h_i (a_i x + b_i y)\)
cites work: The Stability of the Cosine Equation
cites work: Q5514020
cites work: The Functional Equation f(xy) + f(xy -1 ) = 2f(x)f(y) for Groups
cites work: Equations of the form \(H(x\cdot y)=\sum_if_i(x)g_i(y)\)
cites work: The solution of the functional equation of d'Alembert's type for commutative groups
cites work: Regularity properties of exponential polynomials on groups
cites work: Q4002300
cites work: Q5330937
cites work: Q3831390
cites work: On the second part of Hilbert's fifth problem
OpenAlex ID: W1968100397
description: scientific article; zbMATH DE number 699776