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arXiv · 1808.03882

A Whittaker-Plancherel Inversion Formula for $\mathrm{SL}_2(\mathbb{C})$

Zhi Qi·Chang Yang
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Abstract

In this paper, we establish a Whittaker-Plancherel inversion formula for $\mathrm{SL}_2(\mathbb{C})$ 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 $\mathrm{SL}_2(\mathbb{C})$ in terms of its Bessel coefficients attached to irreducible unitary tempered representations of $\mathrm{SL}_2(\mathbb{C})$.

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BibTeXRIS

Zhi Qi, Chang Yang. 2018-08-12. A Whittaker-Plancherel Inversion Formula for $\mathrm{SL}_2(\mathbb{C})$. https://arxiv.org/abs/1808.03882

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