• Korean Journal of Mathematics
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• v.28 no.4
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• pp.649-671
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• 2020

In this paper we give the harmonic analysis associated with the Cherednik operators, next we define and study the Cherednik wavelets and the Cherednik windowed transforms on ℝd, in the W-invariant case, and we prove for these transforms Plancherel and inversion formulas. As application we give these results for the Gaussian Cherednik wavelets and the Gaussian Cherednik windowed transform on ℝd in the W-invariant case.