## Taiwanese Journal of Mathematics

### NORMALIZED SYSTEM FOR WAVE AND DUNKL OPERATORS

#### Abstract

Normalized systems are constructed with respect to wave and Dunkl operators. Non-trivial solutions can thus be built to the equation $Dv(x) + \lambda v(x) = 0$, where $D$ is either the wave operator or the Dunkl operators and $\lambda \in \mathbb{C}$.

#### Article information

Source
Taiwanese J. Math., Volume 14, Number 2 (2010), 675-683.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405813

Digital Object Identifier
doi:10.11650/twjm/1500405813

Mathematical Reviews number (MathSciNet)
MR2655793

Zentralblatt MATH identifier
1218.35060

#### Citation

Liu, Liang; Ren, Guang-Bin. NORMALIZED SYSTEM FOR WAVE AND DUNKL OPERATORS. Taiwanese J. Math. 14 (2010), no. 2, 675--683. doi:10.11650/twjm/1500405813. https://projecteuclid.org/euclid.twjm/1500405813

#### References

• C. F. Dunkl and Y. Xu, Orthogonal Polynomial of Several Variables, Cambridge: Cambridge Univ. Press, 2001.
• V. V. Karachik, Polynomial solutions to the systems of partial differential equations with constant coefficients, Yokohama Math. J., 47 (2000), 121-142.
• V. V. Karachik, Normalized system of functions with respect to the Laplace operator and its applications, J. Math. Anal. Appl., 287 (2003), 577-592.
• G. B. Ren, Almansi decomposition for Dunkl operators, Science in China Ser. A, 48 (2005), 1541-1552.