Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A generalization of d'Alembert's functional equation

Author: Stanley Gudder
Journal: Proc. Amer. Math. Soc. 115 (1992), 419-425
MSC: Primary 39B52; Secondary 81Q05
MathSciNet review: 1098400
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Recent investigations in the foundations of physics have shown that a quantum mechanical influence function satisfies a generalized d'Alembert functional equation. The present paper derives the solutions for this equation on a topological linear space.

References [Enhancements On Off] (What's this?)

  • [1] J. Aczél, Lectures on functional equations and their applications, Academic Press, New York, 1966. MR 0208210 (34:8020)
  • [2] -, On applications and theory of functional equations, Academic Press, New York, 1969.
  • [3] J. Aczél, J. Chung, and C. Ng, Symmetric second differences in product form on groups, Topics in Mathematical Analysis, World Scientific Publ., Singapore, 1989. MR 1116572 (92g:39007)
  • [4] J. Aczél and J. Dhombres, Functional equations in several variables, Encyclopedia Math. Appl., vol., Cambridge Univ. Press, Cambridge, England, 1989. MR 1004465 (90h:39001)
  • [5] J. d'Alembert, Addition au Mémoire sur la courbe que forme une corde tendue mise en vibration, Hist. Acad. Berlin (1750), 355-360.
  • [6] -, Mémoire sur les principles de mécanique, Hist. Acad. Sci. Paris (1769), 278-286.
  • [7] J. A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80, (1980), 411-416. MR 580995 (81m:39015)
  • [8] G. Hemion, A discrete geometry: speculations on a new framework for classical electrodynamics, Intern. J. Theor. Phys. 27 (1988), 1145-1255. MR 966582 (89j:78009)
  • [9] -, Quantum mechanics in a discrete model of classical physics, Intern. J. Theor. Phys. 29 (1990), 1335-1368. MR 1086787 (91m:81013)
  • [10] E. Hewitt and K. Ross, Abstract harmonic analysis vol. I, Academic Press, New York, 1963.
  • [11] E. Hewitt and H. S. Zuckerman, A group-theoretic method in approximation theory, Ann. of Math. (2) 52 (1950), 557-567. MR 0041142 (12:801c)
  • [12] Pl. Kannappan, The functional equation $ f\left( {xy} \right) + f\left( {x{y^{ - 1}}} \right) = 2f\left( x \right)f\left( y \right)$ for groups, Proc. Amer. Math. Soc. 19 (1968), 69-74. MR 0219936 (36:3006)
  • [13] A. Wilansky, Modern methods in topological vector spaces, McGraw-Hill, New York, 1978. MR 518316 (81d:46001)
  • [14] W. Wilson, On certain related functional equations, Bull. Amer. Math. Soc. 26 (1919), 300-312. MR 1560309

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 39B52, 81Q05

Retrieve articles in all journals with MSC: 39B52, 81Q05

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society