The classical Hankel transform in the Kirillov model of the discrete series

Ehud Moshe Baruch

doi:10.1080/10652469.2012.691097

The classical Hankel transform in the Kirillov model of the discrete series

Ehud Moshe Baruch

Mathematics

Technion - Israel Institute of Technology

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

Abstract

In this paper, we give a new and simple proof of the Hankel inversion formula for the classical Hankel transform of index ν which holds for Re(ν)>-1. Using the proof of this formula, we obtain the full description of the Kirillov model for discrete series representations of SL(2, ℝ) and GL(2, ℝ).

Original language	English
Pages (from-to)	339-356
Number of pages	18
Journal	Integral Transforms and Special Functions
Volume	24
Issue number	5
DOIs	https://doi.org/10.1080/10652469.2012.691097
State	Published - May 2013

Keywords

Bessel functions
Hankel transform
Kirillov model
discrete series

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1080/10652469.2012.691097

Cite this

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abstract = "In this paper, we give a new and simple proof of the Hankel inversion formula for the classical Hankel transform of index ν which holds for Re(ν)>-1. Using the proof of this formula, we obtain the full description of the Kirillov model for discrete series representations of SL(2, ℝ) and GL(2, ℝ).",

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AB - In this paper, we give a new and simple proof of the Hankel inversion formula for the classical Hankel transform of index ν which holds for Re(ν)>-1. Using the proof of this formula, we obtain the full description of the Kirillov model for discrete series representations of SL(2, ℝ) and GL(2, ℝ).

KW - Bessel functions

KW - Hankel transform

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KW - discrete series

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M3 - مقالة

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JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

IS - 5

ER -

The classical Hankel transform in the Kirillov model of the discrete series

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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