A Whittaker-Plancherel inversion formula for SL (2, R)

Ehud Moshe Baruch; Zhengyu Mao

doi:10.1016/j.jfa.2006.02.022

A Whittaker-Plancherel inversion formula for SL (2, R)

Ehud Moshe Baruch, Zhengyu Mao

Rutgers Newark, Math & Computer Science

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove a Whittaker-Plancherel inversion formula which gives a Whittaker coefficient of a function on SL (2, R) in terms of certain Bessel coefficients of this function. The Bessel coefficients come from Bessel functions attached to irreducible unitary tempered representations. The Kuznecov transform and Kuznecov inversion formula play a central role in the proof of this Whittaker-Plancherel inversion formula.

Original language	English (US)
Pages (from-to)	221-244
Number of pages	24
Journal	Journal of Functional Analysis
Volume	238
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2006.02.022
State	Published - Sep 1 2006

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Bessel distributions
Bessel functions
Kuznecov transform
Orbital integrals
Whittaker-Plancherel

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10.1016/j.jfa.2006.02.022

Cite this

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title = "A Whittaker-Plancherel inversion formula for SL (2, R)",

abstract = "We prove a Whittaker-Plancherel inversion formula which gives a Whittaker coefficient of a function on SL (2, R) in terms of certain Bessel coefficients of this function. The Bessel coefficients come from Bessel functions attached to irreducible unitary tempered representations. The Kuznecov transform and Kuznecov inversion formula play a central role in the proof of this Whittaker-Plancherel inversion formula.",

keywords = "Bessel distributions, Bessel functions, Kuznecov transform, Orbital integrals, Whittaker-Plancherel",

author = "Baruch, {Ehud Moshe} and Zhengyu Mao",

note = "Funding Information: ✩ This research was supported by Grant No. 2004200 from the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel. * Corresponding author. E-mail addresses: embaruch@math.technion.ac.il (E.M. Baruch), zmao@andromeda.rutgers.edu (Z. Mao). 1 Research of the author was partially supported by NSF grant DMS-0355285 and a NSA grant.",

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AU - Baruch, Ehud Moshe

AU - Mao, Zhengyu

N1 - Funding Information: ✩ This research was supported by Grant No. 2004200 from the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel. * Corresponding author. E-mail addresses: embaruch@math.technion.ac.il (E.M. Baruch), zmao@andromeda.rutgers.edu (Z. Mao). 1 Research of the author was partially supported by NSF grant DMS-0355285 and a NSA grant.

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N2 - We prove a Whittaker-Plancherel inversion formula which gives a Whittaker coefficient of a function on SL (2, R) in terms of certain Bessel coefficients of this function. The Bessel coefficients come from Bessel functions attached to irreducible unitary tempered representations. The Kuznecov transform and Kuznecov inversion formula play a central role in the proof of this Whittaker-Plancherel inversion formula.

AB - We prove a Whittaker-Plancherel inversion formula which gives a Whittaker coefficient of a function on SL (2, R) in terms of certain Bessel coefficients of this function. The Bessel coefficients come from Bessel functions attached to irreducible unitary tempered representations. The Kuznecov transform and Kuznecov inversion formula play a central role in the proof of this Whittaker-Plancherel inversion formula.

KW - Bessel distributions

KW - Bessel functions

KW - Kuznecov transform

KW - Orbital integrals

KW - Whittaker-Plancherel

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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A Whittaker-Plancherel inversion formula for SL (2, R)

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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