Introduction. Whittaker models have been crucial in the development of the theory of automorphic forms. Within the Langlands-Shahidi method, Whittaker models give rise to the definition of local coefficients [Sh1,Sh2], which proved critical in establishing the proof of Langlands’s conjecture relating local L–functions to Plancherel measures for generic representations [Sh3]. This, in turn, led ...

The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L(A) requires the existence of a square-integrable function whose Plancherel transform satisfies Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable funct...

We give the inversion formula and Plancherel for hypergeometric Fourier transform associated with a root system of type $BC$, when multiplicity parameters are not necessarily non-negative.