Abel transform on \(\mathrm{PSL}(2,\mathbb R)\) and some of its applications
type: Item
instance of: scholarly article
title: Abel transform on \(\mathrm{PSL}(2,\mathbb R)\) and some of its applications
zbMATH Open document ID: 1148.22008
author: Rudra P. Sarkar
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2008-09-08T00:00:00Z
review text: The author investigates the use of the Abel transform on \(\text{PSL}(2,\mathbb R)\) as a tool beyond the \(k\)-biinvariant setup, discusses its properties and provides two applications. A notable fact is that the obtained results can be naturally extended to \(\text{SL}(2,\mathbb R)\).
reviewed by: Vladimir Balan
Mathematics Subject Classification ID: 22E43
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 44A12
zbMATH DE Number: 5322628
zbMATH Keywords: Abel transform
zbMATH Keywords: Radon transform
zbMATH Keywords: Helgason-Fourier transform
zbMATH Keywords: spherical functions
zbMATH Keywords: complex measures
MaRDI profile type: Publication
full work available at URL: s12044-008-0018-4
OpenAlex ID: W1968819311
cites work: The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan
cites work: Spherical mean periodic functions on semi simple Lie groups
cites work: Hermite functions and uncertainty principles for the Fourier and the windowed Fourier trans\-forms.
cites work: Q3663816
cites work: Hardy's uncertainty principle on semisimple groups
cites work: Some properties of the Fourier transform on semi-simple Lie groups. I
cites work: The uncertainty principle: A mathematical survey
cites work: Q3829998
cites work: Cramér theorem on symmetric spaces of noncompact type
cites work: A Theorem Concerning Fourier Transforms
cites work: Q3331943
cites work: The Abel, Fourier and Radon transforms on symmetric spaces
cites work: A uniqueness theorem of Beurling for Fourier transform pairs
cites work: A Note on Fourier Transforms
cites work: The heat kernel and Hardy's theorem on symmetric spaces of noncompact type
cites work: A complete analogue of Hardy's theorem on \(SL_2(\mathbb{R})\) and characterization of the heat kernel
cites work: Beurling's theorem for \(\mathrm{SL} (2, {\mathbb{R}})\)
cites work: The Helgason Fourier transform for semisimple Lie groups I: The Case of SL2(ℝ)
cites work: Q4440604
cites work: The uncertainty principle on Riemannian symmetric spaces of the noncompact type
cites work: An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups
cites work: An introduction to the uncertainty principle. Hardy's theorem on Lie groups. With a foreword by Gerald B. Folland
DOI: 10.1007/S12044-008-0018-4
description: scientific article; zbMATH DE number 5322628