A Whittaker–Plancherel inversion formula for SL(2,R) ✩

We prove a Whittaker–Plancherel inversion formula which gives a Whittaker coefficient of a function on SL(2,R) in terms of certain Bessel coefficients of this function. The Bessel coefficients come from Bessel functions attached to irreducible unitary tempered representations. The Kuznecov transform and Kuznecov inversion formula play a central role in the proof of this Whittaker–Plancherel inversion formula. © 2006 Elsevier Inc. All rights reserved.