×

Harmonic analysis associated with the Cherednik operators and the Heckman-Opdam theory. (English) Zbl 1207.33024

Summary: By using the trigonometric Dunkl intertwining operator and its dual introduced by the author in [Adv. Pure Appl. Math. (to appear)], we define and study the hypergeometric translation operators associated with the Cherednik operators \(T_j\), \(j=1,2,\dots,d\). Next with the help of these translation operators, we define and study the hypergeometric convolution product of functions and distributions associated with the operators \(T_j\), \(j=1,2,\dots,d\).

MSC:

33E30 Other functions coming from differential, difference and integral equations
33C67 Hypergeometric functions associated with root systems
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
43A32 Other transforms and operators of Fourier type
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cherednik I., Invent. Math. 106 pp 411– (1991) · Zbl 0725.20012 · doi:10.1007/BF01243918
[2] Cherednik I., Int. Math. Res. Not. 15 pp 733– (1997) · Zbl 0882.22016 · doi:10.1155/S1073792897000482
[3] Heckman G. J., Compos. Math. 64 pp 329– (1987)
[4] Opdam E. M., Acta Math. 175 pp 75– (1995) · Zbl 0836.43017 · doi:10.1007/BF02392487
[5] Schapira B., Geom. Funct. Anal. 18 pp 222– (2008) · Zbl 1147.33004 · doi:10.1007/s00039-008-0658-7
[6] Trimèche K., J. Fourier Anal. Appl. 12 (5) pp 517– (2006) · Zbl 1105.42004 · doi:10.1007/s00041-005-5073-y
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.