On the Fourier inversion formula for the full modular group (Q2889321)
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scientific article; zbMATH DE number 6043175
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Fourier inversion formula for the full modular group |
scientific article; zbMATH DE number 6043175 |
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On the Fourier inversion formula for the full modular group (English)
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7 June 2012
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Eisenstein series
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Fourier inversion
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Plancherel formula
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Maass-Eisenstein wave packets
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modular group
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In the paper under review a new proof of the Fourier inversion formula and the Plancherel formula for Maass-Eisenstein wave packets for the (full) modular group \(SL(2, \mathbb{Z})\) is given. The proof uses a truncation argument, introduced in \textit{B. Casselman} [Proc. Symp. Pure Math. 66(pt.2), 19--25 (1999; Zbl 0930.22012)], and classical and harmonic analysis.NEWLINENEWLINESketches of other proofs of the Plancherel formula by \textit{R. P. Langlands} [Proc. Sympos. Pure Math. 9, 235--252 (1966; Zbl 0204.09603)], \textit{E. Lapid} [Clay Mathematics Proceedings 13, 309--331 (2011; Zbl 1242.22025)] and B. Casselman are presented at the end of the paper for the purpose of comparison.
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