A Whittaker-Plancherel Inversion Formula for $\mathrm{SL}_2(\mathbb{C})$
Representation Theory
2019-11-12 v2
Abstract
In this paper, we establish a Whittaker-Plancherel inversion formula for from the analytic perspective of the Bessel transform of Bruggeman and Motohashi. The formula gives a decomposition of the Whittaker-Fourier coefficient of a compactly supported function on in terms of its Bessel coefficients attached to irreducible unitary tempered representations of .
Cite
@article{arxiv.1808.03882,
title = {A Whittaker-Plancherel Inversion Formula for $\mathrm{SL}_2(\mathbb{C})$},
author = {Zhi Qi and Chang Yang},
journal= {arXiv preprint arXiv:1808.03882},
year = {2019}
}
Comments
17 pages. Analysis greatly simplified thanks to an observation of the referee. To appear in J. Anal. Math