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Summary. Let G be a connected nilpotent Lie Group. We show that the solutions of the short and the long version of d’Alembert’s equation on G have the same form as on abelian groups. Furthermore we show that any solution of Wilson’s equation $$ f(xy) + f(xy^{-1}) = 2f(x)g(y) $$ in the case g ≠ 1 has the form $$ f = A(m + \check{m})/2 + B(m-\check{m})/2 $$ and $$ g = (m + \check{m})/2...
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