An Introduction to Dunkl Theory and Its Analytic Aspects

By Jean-Philippe Anker. 2016

65 citations recorded by the source corpus.

The aims of these lecture notes are twofold. On the one hand, they are meant as an introduction to rational and trigonometric Dunkl theory, starting with the historical examples of special functions associated with radial Fourier analysis on rank one symmetric spaces. On the other hand, we have tried to give an up-to-date account of the main results and problems, with an emphasis on analytic aspects.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cc308efb1b8c9e962a3e8193ea58cbc7881dedb6

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In Applied Mathematics

1. S. Tikhonov
2. V. Ivanov
3. Dmitry V. Gorbachev

In Mathematical Physics

1. S. Tikhonov

Citations in the corpus

• Positive $$L^p$$Lp-Bounded Dunkl-Type Generalized Translation Operator and Its Applications (2017, background): “l weight on Rd and Sd−1 were proved; see, e.g., the papers by C.F. Dunkl [14, 15, 16], M. Ro¨sler [41, 42, 43, 44], M.F.E. de Jeu [24, 25], K. Trim`eche [53, 54], Y. Xu [55, 56], and the recent works [1, 11, 12, 19, 20]. Date: March 21, 2017. 1991 Mathematics Subject Classification. 42B10, 33C45, 33C”