Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

作者：Narayanan E K; Pasquale A^*; Pusti S

来源：Advances in Mathematics, 2014, 252: 227-259.

DOI：10.1016/j.aim.2013.10.027

• Hypergeometric functions
• Harish-Chandra series expansion
• Spherical functions
• Root systems
• Cherednik operators
• Hypergeometric Fourier transform

A series expansion for Heckman-Opdam hypergeometric functions phi(lambda) is obtained for all lambda is an element of alpha(C)*. As a consequence, estimates for phi(lambda) away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The L-P-theory for the hypergeometric Fourier transform is developed for 0 %26lt; p %26lt; 2. In particular, an inversion formula is proved when 1 %26lt;= p %26lt; 2.

• 出版日期2014-2-15