The Helgason Fourier Transform for Symmetric spaces

2003 ◽  
pp. 467-473 ◽  
Author(s):  
Rudra P. Sarkar ◽  
Alladi Sitaram
Keyword(s):  
Fourier Transform ◽  
Symmetric Spaces

Characterization of Dini–Lipschitz functions for the Helgason Fourier transform on rank one symmetric spaces

2016 ◽  
Vol 7 (4) ◽  
Author(s):  
Salah El Ouadih ◽  
Radouan Daher
Keyword(s):  
Fourier Transform ◽  
Symmetric Spaces ◽  
Translation Operator ◽  
Lipschitz Functions ◽  
Generalized Translation Operator ◽  
Generalized Translation ◽  
Rank One

AbstractIn this paper, using a generalized translation operator, we obtain an analog of Younis’ theorem, [

scholarly journals Growth properties of the Fourier transform

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 755-760 ◽  
Author(s):  
William Bray ◽  
Mark Pinsky
Keyword(s):  
Fourier Transform ◽  
Euclidean Space ◽  
Symmetric Spaces ◽  
Bessel Functions ◽  
Spherical Means ◽  
Compact Type ◽  
Growth Property ◽  
Growth Properties ◽  
Rank One ◽  
The Fourier Transform

In a recent paper by the authors, growth properties of the Fourier transform on Euclidean space and the Helgason Fourier transform on rank one symmetric spaces of non-compact type were proved and expressed in terms of a modulus of continuity based on spherical means. The methodology employed first proved the result on Euclidean space and then, via a comparison estimate for spherical functions on rank one symmetric spaces to those on Euclidean space, we obtained the results on symmetric spaces. In this note, an analytically simple, yet overlooked refinement of our estimates for spherical Bessel functions is presented which provides significant improvement in the growth property estimates.

scholarly journals Characterization of Dini Lipschitz Functions in Terms of Their Helgason Transform

2016 ◽  
Vol 54 (2) ◽  
pp. 117-130
Author(s):  
Salah El Ouadih ◽  
Radouan Daher
Keyword(s):  
Fourier Transform ◽  
Lipschitz Condition ◽  
Symmetric Spaces ◽  
Translation Operator ◽  
Lipschitz Functions ◽  
Generalized Translation Operator ◽  
Generalized Translation ◽  
Rank One ◽  
Riemannian Symmetric Spaces

Abstract In this paper, using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [6] for the Helgason Fourier transform of a set of functions satisfying the Dini Lipschitz condition in the space L2 for functions on noncompact rank one Riemannian symmetric spaces.

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