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Short view Article in peer-reviewed journal
Bessel functions for root systems via the trigonometric setting
Ben Said S. et al
International Mathematics Research Notices 9 (2005) 551--585 - http://hal.archives-ouvertes.fr/hal-00095073
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Salem Ben Said ()1, Bent Orsted2
1:  IECN - Institut Elie Cartan Nancy
http://www.iecn.u-nancy.fr/
CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
France
2:  Aarhus University [Aarhus]
http://www.au.dk/en/
Aarhus University
Nordre Ringgade 1 DK-8000 Aarhus C
Denmark
Mathematics/Functional Analysis
Bessel functions for root systems via the trigonometric setting
By taking an appropriate limit, we obtain the Bessel functions related to root systems as limit of Heckman-Opdam hypergeometric functions . A more general class of Bessel functions is also investigated, which we shall call the \Theta-Bessel functions. Explicit formuals for the \Theta-Bessel functions are obtained when the multiplicity functions are even and positive integer-valued. This class encloses the Bessel functions on the tangent space at the origin of non-compact causal symmetric spaces, were an integral representation for these special functions is shown.
English

International Mathematics Research Notices
2005
9
551--585