A note on d'Alembert's functional equation

Mohamed Akkouchi

Annales mathématiques Blaise Pascal (2001)

  • Volume: 8, Issue: 1, page 1-6
  • ISSN: 1259-1734

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Akkouchi, Mohamed. "A note on d'Alembert's functional equation." Annales mathématiques Blaise Pascal 8.1 (2001): 1-6. <http://eudml.org/doc/79225>.

@article{Akkouchi2001,
author = {Akkouchi, Mohamed},
journal = {Annales mathématiques Blaise Pascal},
keywords = {d'Alembert's functional equation; almost-periodic functions},
language = {eng},
number = {1},
pages = {1-6},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {A note on d'Alembert's functional equation},
url = {http://eudml.org/doc/79225},
volume = {8},
year = {2001},
}

TY - JOUR
AU - Akkouchi, Mohamed
TI - A note on d'Alembert's functional equation
JO - Annales mathématiques Blaise Pascal
PY - 2001
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 8
IS - 1
SP - 1
EP - 6
LA - eng
KW - d'Alembert's functional equation; almost-periodic functions
UR - http://eudml.org/doc/79225
ER -

References

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  2. [2] J. Aczèl AND J. Dhombres, Functional Equations in Severables Variables, Encyclopedia of Mathematics and its applications. Cambridge University Press, 1989. Zbl0685.39006MR1004465
  3. [3] M. Akkouchi, A. Bakali AND H. El Qorachi, D'Alembert's functional equation on compact Gel'fand pairs, Maghreb Math. Rev. (To appear). MR1871524
  4. [4] J. D'Alembert, Mémoire sur les principes de la mécanique, Hist. Acad. Sci., Paris, 1769, pp. 278 - 286. 
  5. [5] H. Bohr, Almost Periodic Functions, Chelsea, New York, 1951. Zbl0005.20303MR45238
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  8. [8] Z. Gajda, On functional equations associated with characters of unitary reprsentations of groups, Aequationes Mathematicae, 44, (1992) 109 - 121. Zbl0772.39007MR1165788
  9. [9] E. Hewitt AND K.A. Ross, Abstract harmonic analysis, VOL. I (VOL. 2) Springer-Verlag, Berlin, 1979. (1970). MR551496
  10. [10] PL. Kannappan, On the functional equation f(x + y) + f(x - y) = 2f(x)f(y), Amer. Math. Monthly, 72 (1965) 374 - 377. Zbl0136.12403MR180774
  11. [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. Zbl0169.48102MR219936
  12. [12] Y. Katznelson, An Introduction to Harmonic Analysis, Dover Publications, Inc.New York, 1976 (Second edition). Zbl0352.43001MR422992
  13. [13] E.T. Ljubenova, On D'Alembert's functional equation on an Abelian group, Aequationes Mathematicae, 22, (1981) 54 - 55. Zbl0462.39007MR623317
  14. [14] O'Connor Thomas A. ,A solution of D'Alembert's functional equation on a locally compact group, Aequationes Mathematicae, 15, (1977) 235 - 238. Zbl0384.43009
  15. [15] F.J. Papp, The D'Alembert functional equation on groups, Amer. Math. Monthly, 92, (1985) 273 - 275. Zbl0576.39007MR786527
  16. [16] R.C. Penny AND A.L. Rukhin, D'Alembert's functional equation on groups, Proc. Amer. Math. Soc., 77, (1979) 73 - 80. Zbl0445.39004MR539634
  17. [17] L. Székelyhidi, Almost periodicity and functional equations, Aequationes Mathematicae, 26, (1983) 163 - 175. Zbl0566.39010MR753528
  18. [18] H. Stetkaer, D'Alembert's equation and spherical functions, Aequationes Mathematicae, 48, (1994) 220 - 227. Zbl0810.39008MR1295092
  19. [19] H. Stetkaer, Functional equations on abelian groups with involution, Aequationes Mathematicae, 54, (1997) 144 - 172. Zbl0899.39007MR1466300

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