, Volume 67, Issue 1-2, pp 188-194

Applications of Wilson’s functional equation

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Summary.

We reduce the functional equation

\( f(x + y) - f(x - y) = \sum_{i=1}^{n} g_{i}(x)h_{i}(y) \)

for n = 1, 2, 3 to the matrix equation

\( E(x + y) + E(x - y) = [E(y) + E(-y)]E(x) \)

and we determine the general solutions for n = 2.

Manuscript received: October 7, 2002 and, in final form, May 27, 2003.