English

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 SL2(C)\mathrm{SL}_2(\mathbb{C}) 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 SL2(C)\mathrm{SL}_2(\mathbb{C}) in terms of its Bessel coefficients attached to irreducible unitary tempered representations of SL2(C)\mathrm{SL}_2(\mathbb{C}).

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

R2 v1 2026-06-23T03:31:04.484Z