aequationes mathematicae

, Volume 67, Issue 1–2, pp 12–25 | Cite as

d’Alembert’s and Wilson’s equations on Lie groups

Research paper


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 \( g = (m + \check{m})/2 \) where \( m : G \rightarrow {\mathbb C}^* \) is a homomorphism and A and B are complex constants. Finally we solve Jensen’s equation \( f(xy) + f(xy^{-1}) = 2f(x) \) on a semidirect product of two abelian groups.

Mathematics Subject Classification (2000).



Functional equation d’Alembert Wilson Jensen Nilpotent Lie group. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMississippi State UniversityUSA

Personalised recommendations