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

Access to Document

10.1080/10652469.2012.691097

Cite this

@article{f1e0925f1c1543a68cc7023f03f81186,

title = "The classical Hankel transform in the Kirillov model of the discrete series",

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).",

keywords = "Bessel functions, Hankel transform, Kirillov model, discrete series",

author = "Baruch, {Ehud Moshe}",

note = "Funding Information: This research was partially supported by the Center of Excellence of the Israel Science Foundation (grant no. 1691/10).",

year = "2013",

month = may,

doi = "10.1080/10652469.2012.691097",

language = "الإنجليزيّة",

volume = "24",

pages = "339--356",

journal = "Integral Transforms and Special Functions",

issn = "1065-2469",

publisher = "Taylor and Francis Ltd.",

number = "5",

}

TY - JOUR

T1 - The classical Hankel transform in the Kirillov model of the discrete series

AU - Baruch, Ehud Moshe

N1 - Funding Information: This research was partially supported by the Center of Excellence of the Israel Science Foundation (grant no. 1691/10).

PY - 2013/5

Y1 - 2013/5

N2 - 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).

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

KW - Kirillov model

KW - discrete series

UR - http://www.scopus.com/inward/record.url?scp=84877842846&partnerID=8YFLogxK

U2 - 10.1080/10652469.2012.691097

DO - 10.1080/10652469.2012.691097

M3 - مقالة

SN - 1065-2469

VL - 24

SP - 339

EP - 356

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

Access to Document

Other files and links

Fingerprint

Cite this