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)



Duhamel solutions of non-homogeneous $ q^2$-analogue wave equations

Author: Richard L. Rubin
Journal: Proc. Amer. Math. Soc. 135 (2007), 777-785
MSC (2000): Primary 39A12; Secondary 33D15, 42A38
Published electronically: August 31, 2006
MathSciNet review: 2262873
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: $ q$-analogue non-homogeneous wave equations are solved by a Duhamel solution strategy using constructions with $ q$-analogue Fourier multipliers to compensate for the dependence of the analogue differential Leibnitz rule on the parity of the functions involved.

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

  • 1. J. Bustoz and J. L. Cardoso, Basic analog of Fourier series on a $ q$-linear grid, J. Approx. Theory 112 no. 1, (2001), pp. 134-157. MR 1857606 (2002j:33015a)
  • 2. M. Fichtmuller and W. Weich, The limit transition $ q \to 1$ of the $ q$-Fourier transform, J. Math. Phys. 37 (1996), 4683-4689. MR 1408114 (97j:33039)
  • 3. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia Math. Appl., vol. 35, Cambridge Univ. Press, Cambridge, 1990. MR 1052153 (91d:33034)
  • 4. G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1964.
  • 5. Y. Katznelson, An introduction to harmonic analysis. Wiley, New York-London-Sydney 1968. MR 0248482 (40:1734)
  • 6. T. H. Koornwinder and R. F. Swarttouw, On $ q$-Analogues of the Fourier and Hankel Transforms, Trans. Amer. Math. Soc. 333 (1992), 445-461. MR 1069750 (92k:33013)
  • 7. R. L. Rubin, A $ q^2$-Analogue Operator for $ q^2$-Analogue Fourier Analysis, J. Math. Anal. Appl. 212 (1997), 571-582. MR 1464898 (99g:33050)
  • 8. E. M. Stein, G. Weiss, Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series, No. 32. Princeton University Press, Princeton, N.J., 1971. MR 0304972 (46:4102)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 39A12, 33D15, 42A38

Retrieve articles in all journals with MSC (2000): 39A12, 33D15, 42A38

Additional Information

Richard L. Rubin
Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199

Received by editor(s): January 22, 2004
Received by editor(s) in revised form: March 28, 2005, and October 10, 2005
Published electronically: August 31, 2006
Communicated by: Andreas Seeger
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society