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The Continuous Wavelet Transform Associated with a Dunkl Type Operator on the Real Line
Department of Mathematics, College of Sciences for Girls, University of Dammam, Dammam, KSA
Department of Mathematics, College of Sciences for Girls, University of Dammam, Dammam, KSA
- 1 Department of Mathematics, College of Sciences for Girls, University of Dammam, Dammam, KSA
- 2 Department of Mathematics, College of Sciences for Girls, University of Dammam, Dammam, KSA
Advances in Pure Mathematics·Volume 03 (2013)·Pages 443–450·Published 23 July 2013·DOI10.4236/apm.2013.35063
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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/d x .
KeywordsDifferential-Difference OperatorGeneralized WaveletsGeneralized Continuous Wavelet Transform
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