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2014 | OriginalPaper | Chapter

The Radon Transform and Its Dual for Limits of Symmetric Spaces

Authors : Joachim Hilgert, Gestur Ólafsson

Published in: Developments and Retrospectives in Lie Theory

Publisher: Springer International Publishing

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Abstract

The Radon transform and its dual are central objects in geometric analysis on Riemannian symmetric spaces of the noncompact type. In this article we study algebraic versions of those transforms on inductive limits of symmetric spaces. In particular, we show that normalized versions exists on some spaces of regular functions on the limit. We give a formula for the normalized transform using integral kernels and relate them to limits of double fibration transforms on spheres.

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previous chapter Harmonic Analysis on Homogeneous Complex Bounded Domains and Noncommutative Geometry

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Title: The Radon Transform and Its Dual for Limits of Symmetric Spaces
Authors: Joachim Hilgert
Gestur Ólafsson
Publisher: Springer International Publishing
Book: Developments and Retrospectives in Lie Theory
Print ISBN: 978-3-319-09933-0

Electronic ISBN: 978-3-319-09934-7

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-09934-7_3

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