Duhamel solutions of non-homogeneous $q^2$-analogue wave equations
HTML articles powered by AMS MathViewer
- by Richard L. Rubin PDF
- Proc. Amer. Math. Soc. 135 (2007), 777-785 Request permission
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
- J. Bustoz and J. L. Cardoso, Basic analog of Fourier series on a $q$-linear grid, J. Approx. Theory 112 (2001), no. 1, 134–157. MR 1857606, DOI 10.1006/jath.2001.3599
- M. Fichtmüller and W. Weich, The limit transition $q\to 1$ of the $q$-Fourier transform, J. Math. Phys. 37 (1996), no. 9, 4683–4689. MR 1408114, DOI 10.1063/1.531647
- George Gasper and Mizan Rahman, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 35, Cambridge University Press, Cambridge, 1990. With a foreword by Richard Askey. MR 1052153
- G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1964.
- Yitzhak Katznelson, An introduction to harmonic analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0248482
- Tom H. Koornwinder and René F. Swarttouw, On $q$-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. 333 (1992), no. 1, 445–461. MR 1069750, DOI 10.1090/S0002-9947-1992-1069750-0
- Richard L. Rubin, A $q^2$-analogue operator for $q^2$-analogue Fourier analysis, J. Math. Anal. Appl. 212 (1997), no. 2, 571–582. MR 1464898, DOI 10.1006/jmaa.1997.5547
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 777-785
- MSC (2000): Primary 39A12; Secondary 33D15, 42A38
- DOI: https://doi.org/10.1090/S0002-9939-06-08525-X
- MathSciNet review: 2262873