MELLIN TRANSFORMS OF WHITTAKER FUNCTIONS

Let G be a connected reductive algebraic group defined and quasi-split over R. In this paper the Mellin transform of the Whittaker function associated to G is studied. It is shown that this Mellin transform has a meromorphic continuation and satisfies certain explicit difference equations. An effective algorithm for obtaining these difference equations is presented, and is illustrated in low rank cases for G = GL(n).