Bessel functions for root systems via the trigonometric setting

Salem Ben Said (1) , Bent Orsted (2)

1 IECN - Institut Élie Cartan de Nancy
2 Aarhus University [Aarhus]

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.

Domaines: Analyse fonctionnelle [math.FA]

Salem Ben Said, Bent Orsted. Bessel functions for root systems via the trigonometric setting. International Mathematics Research Notices, 2005, 9, pp.551--585. ⟨hal-00095073⟩