The Continuous Wavelet Transform Associated with a Dunkl Type Operator on the Real Line

Copyright © 2013 E. A. Al Zahrani, M. A. Mourou. This is an open access article distributed under the Creative Commons Attribu-tion License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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 wave-let 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