Geodesic
Solution of a functional equation on compact groups using Fourier analysis
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 69 (2015) no. 2.

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Let G be a compact group, let n ∈ N∖{0,1} be a fixed element and let σ be a continuous automorphism on G such that σ^n=I. Using the non-abelian Fourier transform, we determine the non-zero continuous solutions f:G → C of the functional equation f(xy)+∑_k=1^n-1f(σ^k(y)x)=nf(x)f(y), x,y ∈ G, in terms of unitary characters of G.
Keywords: Functional equation, non-abelian Fourier transform, representation of a compact group. 
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Chahbi, Abdellatif; Fadli, Brahim; Kabbaj, Samir. Solution of a functional equation on compact groups using Fourier analysis. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 69 (2015) no. 2. http://geodesic.mathdoc.fr/item/AUM_2015_69_2_a4/

[1] Akkouchi, M., Bouikhalene, B., Elqorachi, E., Functional equations and K-spherical functions, Georgian Math. J. 15 (2008), 1-20.

[2] An, J., Yang, D.,Nonabelian harmonic analysis and functional equations on compact groups, J. Lie Theory 21 (2011), 427-455.

[3] Badora, R., On a joint generalization of Cauchy's and d'Alembert's functional equations, Aequationes Math. 43 (1992), 72-89.

[4] Chahbi, A., Fadli, B., Kabbaj, S., Functional equations of Cauchy's and d'Alembert's type on compact groups, Proyecciones (Antofagasta) 34 (2015), 297-305.

[5] Chojnacki, W., On some functional equation generalizing Cauchy's and d'Alembert's functional equations, Colloq. Math. 55 (1988), 169-178.

[6] Chojnacki, W., On group decompositions of bounded cosine sequences, Studia Math. 181 (2007), 61-85.

[7] Chojnacki, W., On uniformly bounded spherical functions in Hilbert space, Aequationes Math. 81 (2011), 135-154.

[8] Fadli, B., Zeglami, D., Kabbaj, S., A variant of Wilson's functional equation, Publ. Math. Debrecen, to appear.

[9] Davison, T. M. K., D'Alembert's functional equation on topological groups, Aequationes Math. 76 (2008), 33-53.

[10] Davison, T. M. K., D'Alembert's functional equation on topological monoids, Publ. Math. Debrecen, 75 (2009), 41-66.

[11] de Place Friis, P., D'Alembert's and Wilson's equation on Lie groups, Aequationes Math. 67 (2004), 12-25.

[12] Elqorachi, E., Akkouchi, M., Bakali, A., Bouikhalene, B., Badora's equation on non-Abelian locally compact groups, Georgian Math. J. 11 (2004), 449-466.

[13] Folland, G., A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, FL, 1995.

[14] Shin'ya, H., Spherical matrix functions and Banach representability for locally compact motion groups, Japan. J. Math. (N.S.), 28 (2002), 163-201.

[15] Stetkaer, H., D'Alembert's functional equations on metabelian groups, Aequationes Math. 59 (2000), 306-320.

[16] Stetkaer, H., D'Alembert's and Wilson's functional equations on step 2 nilpotent groups, Aequationes Math. 67 (2004), 241-262.

[17] Stetkaer, H., Properties of d'Alembert functions, Aequationes Math. 77 (2009), 281-301.

[18] Stetkaer, H., Functional Equations on Groups, World Scientfic, Singapore, 2013.

[19] Stetkaer, H., D'Alembert's functional equation on groups, Banach Center Publ. 99 (2013), 173-191.

[20] Stetkaer, H., A variant of d'Alembert's functional equation, Aequationes Math. 89 (2015), 657-662.

[21] Yang, D., Factorization of cosine functions on compact connected groups, Math. Z. 254 (2006), 655-674.

[22] Yang, D., Functional equations and Fourier analysis, Canad. Math. Bull. 56 (2013), 218-224.