Sonine Transform Associated to the Dunkl Kernel on the Real Line
Copyright policy )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 $\mathbb{R}$. 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 give a Plancherel formula for the operator ${}^tS_{α,β}$.
This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
- National University United States
- Tunis El Manar University Tunisia
Dunkl Sonine transform, Dunkl transform, \(L^p\)-spaces and other function spaces on groups, semigroups, etc., Dunkl intertwining operator, complex powers of the Dunkl Laplacian, Mathematics - Classical Analysis and ODEs, QA1-939, Other transforms and operators of Fourier type, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics, Harmonic analysis on hypergroups, Dunkl sonine transform
Dunkl Sonine transform, Dunkl transform, \(L^p\)-spaces and other function spaces on groups, semigroups, etc., Dunkl intertwining operator, complex powers of the Dunkl Laplacian, Mathematics - Classical Analysis and ODEs, QA1-939, Other transforms and operators of Fourier type, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics, Harmonic analysis on hypergroups, Dunkl sonine transform
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