Sonine Transform Associated to the Dunkl Kernel on the Real Line
We consider the Dunkl intertwining operator V_α and its dual ^tV_α, we define and study the Dunkl Sonine operator and its dual on R. Next, we introduce complex powers of the Dunkl Laplacian Δ_α and establish inversion formulas for the Dunkl Sonine operator S_{α,β} and its dual ^tS_{α,β}. Also, we gi...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2008-12-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2008.092 |