Proceedings of the American Mathematical Society

Author(s): Pavlos Sinopoulos
Journal: Proc. Amer. Math. Soc. 125 (1997), 1089-1094.
MSC (1991): Primary 39B42, 39B52, 39B62
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$\begin{displaymath}f(x+y)+f(x-y) =A(y)f(x)\qquad (x,y\in G), \end{displaymath}$

where

is a 2-divisible abelian group, $f$

is a vector-valued function and $A$

is a matrix-valued function. Using this result we solve the scalar equation

$\begin{displaymath}f(x+y)+f(x-y)=g_1(x)h_1(y)+g_2(x) h_2(y)\qquad (x,y\in G), \end{displaymath}$

which contains as special cases, among others, the d'Alembert and Wilson equations and the parallelogram law.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 39B42, 39B52, 39B62

Stetkær, Henrik, Trigonometric functional equations of rectangular type, Aequationes Math. (3) 56 (1998), 251--270. (English) MR 99j:39025

Stetkær, Henrik, D'Alembert's and Wilson's functional equations for vector and $2\times 2$ matrix valued functions, Math. Scand. (1) 87 (2000), 115--132. (English) MR CMP Issue 2000:17

Corovei, Ilie, Wilson's functional equation on $P\sb 3$-groups, Aequationes Math. (3) 61 (2001), 212--220. MR CMP 1 833 141

Elhoucien Elqorachi and Mohamed Akkouchi, On generalized d ’Alembert and Wilson functional equations, Aequationes Math. 66 (2003), 241 –256. MR 2028561

Pavlos Sinopoulos, Wilson's functional equation in dimension 3, Aequationes Math. 66 (2003), 164-179. MR 2003463

Sinopoulos, Pavlos, Applications of Wilson's functional equation, Aequationes Math. 67 (2004), 188--194. MR 2049617

Pavlos Sinopoulos, Applications of Wilson's functional equation. II, Nonlinear Funct. Anal. Appl. (2) 10 (2005), 201--212. (English) MR 2167108

Stetkær, Henrik , Functional equations and matrix-valued spherical functions, Aequationes Math. 69 (2005), 271--292. MR MR2139609

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