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

DOI: 10.4236/apm.2013.35063   PDF   HTML   XML   3,209 Downloads   6,107 Views   Citations

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.

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E. Zahrani and M. Mourou, "The Continuous Wavelet Transform Associated with a Dunkl Type Operator on the Real Line," Advances in Pure Mathematics, Vol. 3 No. 5, 2013, pp. 443-450. doi: 10.4236/apm.2013.35063.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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