Wilson's functional equation for vector and matrix functions
Author:
Pavlos Sinopoulos
Journal:
Proc. Amer. Math. Soc. 125 (1997), 10891094
MSC (1991):
Primary 39B42, 39B52, 39B62
MathSciNet review:
1363186
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Abstract 
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Abstract: We determine the general solution of the functional equation where is a 2divisible abelian group, is a vectorvalued function and is a matrixvalued function. Using this result we solve the scalar equation which contains as special cases, among others, the d'Alembert and Wilson equations and the parallelogram law.
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 J. Aczél, J. K. Chung and C. T. Ng, Symmetric second differences in product form on groups, Topics in mathematical analysis, (edited by Th. M. Rassias), World Scientific Publ., 1989, pp. 122. MR 92g:39007
 2.
 J. Aczél and J. Dhombres, Functional equations in several variables, Cambridge Univ. Press, 1989. MR 90h:39001
 3.
 J. K. Chung, Pl. Kannappan and C. T. Ng, On two trigonometric functional equations, Math. Rep. Toyama Univ. 11 (1988), 153165. MR 89j:39010
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 A. L. Rukhin, The solution of the functional equation of d'Alembert's type for commutative groups, Intern. J. Math. Sci. 5 (1982), 315335. MR 84g:39006
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 P. Sinopoulos, Generalized sine equations, I, Aeq. Mathematicae 48 (1994), 171193. MR 95i:39020
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 P. Sinopoulos, Generalized sine equations, II, Aeq. Mathematicae 49 (1995), 122152. MR 96b:39020
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 P. Sinopoulos, A functional equation in three variables for five unknown functions, Submitted.
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 D. A. Suprunenco and R. I. Tyshkevich, Commutative matrices, Academic Press, 1968.
 9.
 W. H. Wilson, On certain related functional equations, Bull. Amer. Math. Soc. 26 (191920), 300312.
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Additional Information
Pavlos Sinopoulos
Affiliation:
18 Vergovitsas Street, GR11475 Athens, Greece
DOI:
http://dx.doi.org/10.1090/S000299399703685X
PII:
S 00029939(97)03685X
Received by editor(s):
August 4, 1995
Received by editor(s) in revised form:
September 22, 1995
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1997
American Mathematical Society
