Generalized wavelet transform associated with the Heckman-Opdam-Jacobi theory on \(\mathbb{R}^{d+1}\) (Q2048960)

With the previous related works in hindsight, the author has attempted to answer the query that whether the theory of wavelets transforms can be extend to the realm of Heckman-Opdam-Jacobi theory on \(\mathbb R^{d+1}\). Foremostly, the author has introduced the harmonic analysis associated with the Heckman-Opdam-Jacobi operator on \(\mathbb R^{d+1}\) in the \(W\)-invariant case. Nextly, the author has investigated upon the generalized wavelet transform associated with the Heckman-Opdam-Jacobi operator. In the sequel, the fundamental properties for the proposed generalized wavelet transform including the Plancherel and inversion formulae are also obtained.