A note on d'Alembert's functional equation
Akkouchi, Mohamed
Annales mathématiques Blaise Pascal, Tome 8 (2001), p. 1-6 / Harvested from Numdam
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Publié le : 2001-01-01
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     author = {Akkouchi, Mohamed},
     title = {A note on d'Alembert's functional equation},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {8},
     year = {2001},
     pages = {1-6},
     mrnumber = {1863643},
     zbl = {0991.39010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2001__8_1_1_0}
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Akkouchi, Mohamed. A note on d'Alembert's functional equation. Annales mathématiques Blaise Pascal, Tome 8 (2001) pp. 1-6. http://gdmltest.u-ga.fr/item/AMBP_2001__8_1_1_0/

[1] J. Aczèl, Vorlesungen über Funktionalgleichungen une ihre Anwendungen, Birkhäuser, basel, 1961. | MR 124647 | Zbl 0096.09102

[2] J. Aczèl AND J. Dhombres, Functional Equations in Severables Variables, Encyclopedia of Mathematics and its applications. Cambridge University Press, 1989. | MR 1004465 | Zbl 0685.39006

[3] M. Akkouchi, A. Bakali AND H. El Qorachi, D'Alembert's functional equation on compact Gel'fand pairs, Maghreb Math. Rev. (To appear). | MR 1871524

[4] J. D'Alembert, Mémoire sur les principes de la mécanique, Hist. Acad. Sci., Paris, 1769, pp. 278 - 286.

[5] H. Bohr, Almost Periodic Functions, Chelsea, New York, 1951. | MR 45238

[6] C. Corduneanu, Almost Periodic Functions, Interscience Publishers, New York, London, Toronto, 1968. | MR 481915 | Zbl 0175.09101

[7] I. Corovei, The cosine functional equation for nilpotent groups, Aequationes Mathematicae, 15, (1977) 99 - 106. | MR 435645 | Zbl 0348.39004

[8] Z. Gajda, On functional equations associated with characters of unitary reprsentations of groups, Aequationes Mathematicae, 44, (1992) 109 - 121. | MR 1165788 | Zbl 0772.39007

[9] E. Hewitt AND K.A. Ross, Abstract harmonic analysis, VOL. I (VOL. 2) Springer-Verlag, Berlin, 1979. (1970). | MR 551496

[10] Pl. Kannappan, On the functional equation f(x + y) + f(x - y) = 2f(x)f(y), Amer. Math. Monthly, 72 (1965) 374 - 377. | MR 180774 | Zbl 0136.12403

[11] Pl. Kannappan, On the functional equation f(xy) + f(xy-1) = 2f(x)f(y) for groups, Proc. Amer. Math. Soc, 19 (1968) 69 - 74. | MR 219936 | Zbl 0169.48102

[12] Y. Katznelson, An Introduction to Harmonic Analysis, Dover Publications, Inc. New York, 1976 (Second edition). | MR 422992 | Zbl 0352.43001

[13] E.T. Ljubenova, On D'Alembert's functional equation on an Abelian group, Aequationes Mathematicae, 22, (1981) 54 - 55. | MR 623317 | Zbl 0462.39007

[14] O'Connor Thomas A. ,A solution of D'Alembert's functional equation on a locally compact group, Aequationes Mathematicae, 15, (1977) 235 - 238. | Zbl 0384.43009

[15] F.J. Papp, The D'Alembert functional equation on groups, Amer. Math. Monthly, 92, (1985) 273 - 275. | MR 786527 | Zbl 0576.39007

[16] R.C. Penny AND A.L. Rukhin, D'Alembert's functional equation on groups, Proc. Amer. Math. Soc., 77, (1979) 73 - 80. | MR 539634 | Zbl 0445.39004

[17] L. Székelyhidi, Almost periodicity and functional equations, Aequationes Mathematicae, 26, (1983) 163 - 175. | MR 753528 | Zbl 0566.39010

[18] H. Stetkaer, D'Alembert's equation and spherical functions, Aequationes Mathematicae, 48, (1994) 220 - 227. | MR 1295092 | Zbl 0810.39008

[19] H. Stetkaer, Functional equations on abelian groups with involution, Aequationes Mathematicae, 54, (1997) 144 - 172. | MR 1466300 | Zbl 0899.39007