A Whittaker-Plancherel Inversion Formula for SL₂(ℂ)

2018/08/12 by Zhi Qi, Qi, Zhi, Chang Yang +1
Mathematics · #22E46 #33C10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1808.03882

openalex publication_date 2018/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish a Whittaker-Plancherel inversion formula for SL₂(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) in terms of its Bessel coefficients attached to irreducible unitary tempered representations of SL₂(ℂ).

Citations

• On the Whittaker Plancherel Theorem for Real Reductive Groups

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