TITLE:
The Continuous Wavelet Transform Associated with a Dunkl Type Operator on the Real Line
AUTHORS:
E. A. Al Zahrani, M. A. Mourou
KEYWORDS:
Differential-Difference Operator; Generalized Wavelets; Generalized Continuous Wavelet Transform
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.5,
July
23,
2013
ABSTRACT: We consider a
singular differential-difference operator Λ on R which includes as a
particular case the one-dimensional Dunkl operator. By using harmonic analysis
tools corresponding to Λ, we introduce and study a new continuous wavelet
transform on R tied to Λ. Such a wavelet transform is exploited to
invert an intertwining operator between Λ and the first derivative operator d/dx.