Geodesic
Nonabelian Harmonic Analysis and Functional Equations on Compact Groups
Jinpeng An1 ; Dilian Yang2
1LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P.R.China
2Dept. of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4, Canada
Journal of Lie Theory, Tome 21 (2011) no. 2, pp. 427-456

Voir la notice de l'article provenant de la source Heldermann Verlag

Making use of nonabelian harmonic analysis and representation theory, we solve the functional equation
f1(xy) + f2(yx) + f3(xy-1) + f4(y-1x) = f5(x)f6(y)
on arbitrary compact groups, where all fi's are unknown square integrable functions. It turns out that the structure of its general solution is analogous to that of linear differential equations. Consequently, various special cases of the above equation, in particular, the Wilson equation and the d'Alembert long equation, are solved on compact groups.
Classification : 39B52, 22C05, 43A30, 22E45
Mots-clés : Functional equation, Fourier transform, representation theory

Jinpeng An  1   ; Dilian Yang  2

1 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P.R.China
2 Dept. of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4, Canada 
Jinpeng An; Dilian Yang. Nonabelian Harmonic Analysis and Functional Equations on Compact Groups. Journal of Lie Theory, Tome 21 (2011) no. 2, pp. 427-456. http://geodesic.mathdoc.fr/item/JOLT_2011_21_2_a7/
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     author = {Jinpeng An and Dilian Yang},
     title = {Nonabelian {Harmonic} {Analysis} and {Functional} {Equations} on {Compact} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {427--456},
     year = {2011},
     volume = {21},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2011_21_2_a7/}
}
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