Abel transform on \(\mathrm{PSL}(2,\mathbb R)\) and some of its applications

DOI10.1007/s12044-008-0018-4zbMath1148.22008OpenAlexW1968819311MaRDI QIDQ943031

Rudra P. Sarkar

Publication date: 8 September 2008

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-008-0018-4

zbMATH Keywords

Radon transformspherical functionscomplex measuresHelgason-Fourier transformAbel transform

Mathematics Subject Classification ID

Radon transform (44A12) Analysis on real and complex Lie groups (22E30) Structure and representation of the Lorentz group (22E43)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The heat kernel and Hardy's theorem on symmetric spaces of noncompact type
• Some properties of the Fourier transform on semi-simple Lie groups. I
• The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan
• The Abel, Fourier and Radon transforms on symmetric spaces
• Beurling's theorem for \(\mathrm{SL} (2, {\mathbb{R}})\)
• Spherical mean periodic functions on semi simple Lie groups
• A uniqueness theorem of Beurling for Fourier transform pairs
• Cramér theorem on symmetric spaces of noncompact type
• The uncertainty principle: A mathematical survey
• An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups
• Hermite functions and uncertainty principles for the Fourier and the windowed Fourier trans\-forms.
• An introduction to the uncertainty principle. Hardy's theorem on Lie groups. With a foreword by Gerald B. Folland
• Hardy's uncertainty principle on semisimple groups
• A complete analogue of Hardy's theorem on \(SL_2(\mathbb{R})\) and characterization of the heat kernel
• The uncertainty principle on Riemannian symmetric spaces of the noncompact type
• A Theorem Concerning Fourier Transforms
• A Note on Fourier Transforms
• The Helgason Fourier transform for semisimple Lie groups I: The Case of SL₂(ℝ)

This page was built for publication: Abel transform on \(\mathrm{PSL}(2,\mathbb R)\) and some of its applications