Abstract
If \({f, g : G \to \mathbb{C}}\), f ≠ 0, is a solution of Wilson’s functional equation on a group G, then g is a d’Alembert function.
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Aczél, J.: Lectures on functional equations and their applications. In: Mathematics in Science and Engineering, vol. 19, pp. xx+510. Academic Press, New York (1966)
Corovei I.: The functional equation f(xy) + f(yx) + f(xy −1) + f(y −1 x) = 4f(x)f(y) for nilpotent groups. Bul. Ştiinţ. Inst. Politeh. Cluj-Napoca Ser. Mat.-Fiz.-Mec. Apl. 20, 25–28 (1978)
Davison T.M.K.: D’Alembert’s functional equation on topological monoids. Publ. Math. Debr. 75(1/2), 41–66 (2009)
Ebanks, B.R., Stetkær, H.: On Wilson’s functional equations. Aequ. Math. (2014). doi:10.1007/s00010-014-0287-1
de Friis P.P.: d’Alembert’s and Wilson’s functional equations on Lie groups. Aequ. Math. 67, 12–25 (2004)
Stetkær H.: d’Alembert’s and Wilson’s functional equations on step 2 nilpotent groups. Aequ. Math. 67(3), 241–262 (2004)
Stetkær H.: Functional Equations on Groups. World Scientific Publishing Co, Singapore (2013)
Yang D.: Functional equations and Fourier analysis. Can. Math. Bull. 56(1), 218–224 (2013)
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Stetkær, H. A link between Wilson’s and d’Alembert’s functional equations. Aequat. Math. 90, 407–409 (2016). https://doi.org/10.1007/s00010-015-0336-4
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DOI: https://doi.org/10.1007/s00010-015-0336-4