On Harish-Chandra theory of global nonsymmetric functions

This paper is devoted to the Harish-Chandra-type decomposition of the global nonsymmetric spherical functions in terms of their asymptotic expansions and the q,t-generalization of the celebrated c-function. This is for any reduced root systems in the q,t-setting; we pay special attention to the case of A1, where this decomposition is very explicit.