On inversion of the Bessel and Gelfand transforms (Q2759080)

The authors study spaces of functions on the groups of \(F\)-rational points of connected reductive algebraic groups defined over a non-Archimedean local field \(F\). In particular, the space of functions related to the Bessel model on the split special orthogonal group of odd degree \(\geq 5\) and the space related to the Whittaker model on a general split connected reductive group are considered. The Fourier transforms are defined, and the Plancherel measures are constructed. An inversion formula is proved which expresses the integral transform in terms of the Satake transform.