Advances in Pure Mathematics
Volume 3, Issue 5 (August 2013)
ISSN Print: 2160-0368 ISSN Online: 2160-0384
Google-based Impact Factor: 0.50 Citations h5-index & Ranking
The Continuous Wavelet Transform Associated with a Dunkl Type Operator on the Real Line ()
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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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