Inversion of the generalized Dunkl intertwining operator on \(\mathbb{R}\) and its dual using generalized wavelets. (English) Zbl 1211.42030
Summary: We establish an inversion formula for a continuous wavelet transform associated with a class of singular differential-difference operators on \(\mathbb{R}\). We apply this result to derive new expressions for the inverse generalized Dunkl intertwining operator and its dual on \(\mathbb{R}\).
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42C15 | General harmonic expansions, frames |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
