Some new estimates for the Helgason-Fourier transform on rank 1 symmetric spaces
type: Item
instance of: scholarly article
title: Some new estimates for the Helgason-Fourier transform on rank 1 symmetric spaces
zbMATH Open document ID: 1405.44001
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2018-07-31T00:00:00Z
review text: In this paper, useful estimates are proved for the Fourier transform in the space of square integrable functions on certain classes of functions, characterized by the generalized continuity modulus, employing a translation operator. It is observed that the Helgason-Fourier transform on an arbitrary Riemannian symmetric space of noncompact type is defined by spherical functions, see [\textit{S. Helgason}, Differential geometry and symmetric spaces. Übersetzung aus dem Englischen von A. L. Oniscik. Moskau: Verlag `Mir'. 533 S. (1964; Zbl 0122.39901)]. Definitions and fundamental regarding the Helgason-Fourier transform are given in Section 2, whereas the main results, in the form of three theorems, proposed estimation for square integrable functions. Reviewer's remark: It may be noticed that reference by \textit{S. Helgason} [Differential geometry, Lie groups, and symmetric spaces. Pure and Applied Mathematics, 80. New York-San Francisco-London: Academic Press. XV, 628 p. (1978; Zbl 0451.53038)] is not A. V. Abilov et al. as typed by the authors in the first line of Section 1 (Introduction). There are two other references for V. A. Abilov et al. An errata may be useful for readers to avoid confusion.
reviewed by: Deshna Loonker
Mathematics Subject Classification ID: 44A05
zbMATH DE Number: 6911923
zbMATH Keywords: Helgason Fourier transform
zbMATH Keywords: square integrable functions, symmetric space
zbMATH Keywords: generalized translation operator
author: Radouan Daher
author: S. El Ouadih
MaRDI profile type: Publication
full work available at URL: s12044-018-0409-0
OpenAlex ID: W2808208973
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DOI: 10.1007/S12044-018-0409-0
description: scientific article; zbMATH DE number 6911923