Wilson's functional equation

for vector and matrix functions

Author:
Pavlos Sinopoulos

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1089-1094

MSC (1991):
Primary 39B42, 39B52, 39B62

MathSciNet review:
1363186

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Abstract | References | Similar Articles | Additional Information

Abstract: We determine the general solution of the functional equation

where is a 2-divisible abelian group, is a vector-valued function and is a matrix-valued 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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Additional Information

**Pavlos Sinopoulos**

Affiliation:
18 Vergovitsas Street, GR-11475 Athens, Greece

DOI:
https://doi.org/10.1090/S0002-9939-97-03685-X

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