Fourier Transforms of Dini–Lipschitz Functions on Rank 1 Symmetric Spaces

2016 ◽  
Vol 13 (6) ◽  
pp. 4401-4411 ◽  
Author(s):  
S. Fahlaoui ◽  
M. Boujeddaine ◽  
M. El Kassimi
Keyword(s):  
Symmetric Spaces ◽  
Fourier Transforms ◽  
Lipschitz Functions

scholarly journals Fourier transforms of Lipschitz functions on the hyperbolic planeH2

1998 ◽  
Vol 21 (2) ◽  
pp. 397-401 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Hyperbolic Plane ◽  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Order Of Magnitude ◽  
Complex Valued ◽  
Lipschitz Conditions

The purpose of the present work is to study the order of magnitude of the Fourier transformsfˆ(λ)for largeλof complex-valued functionsf(z)sating certain Lipschitz conditions in the non-Euclidean hyperbolic planeH2.

scholarly journals Titchmarsh theorems for Fourier transforms of Hölder–Lipschitz functions on compact homogeneous manifolds

2019 ◽  
Vol 189 (1) ◽  
pp. 23-49 ◽  
Author(s):  
Radouan Daher ◽  
Julio Delgado ◽  
Michael Ruzhansky
Keyword(s):  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Homogeneous Manifolds

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 Fourier transforms of Dini-Lipschitz functions

1986 ◽  
Vol 9 (2) ◽  
pp. 301-312 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Fourier Series ◽  
Dual Space ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Fourier Transforms ◽  
Function Class ◽  
Lipschitz Functions ◽  
Lipschitz Class ◽  
The Absolute ◽  
Lipschitz Conditions

It is well known that if Lipschitz conditions of a certain order are imposed on a functionf(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms off. In general, iff(x)belongs to a certain function class, then the Lipschitz conditions have bearing as to the dual space to which the Fourier coefficients and transforms off(x)belong. In the present work we do study the same phenomena for the wider Dini-Lipschitz class as well as for some other allied classes of functions.

scholarly journals The Fourier transforms of Lipschitz functions on certain domains

1997 ◽  
Vol 20 (4) ◽  
pp. 817-822 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Motion Group ◽  
Hankel Transforms

The Fourier transforms of certain Lipschitz functions are discussed and compared with the Hankel transforms of these functions and with their Fourier transforms on the Euclidean Cartan Motion groupM(n),n≥2.

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.

scholarly journals Fourier transforms of Dini-Lipschitz functions on Vilenkin groups

1992 ◽  
Vol 15 (3) ◽  
pp. 609-612
Author(s):  
M. S. Younis
Keyword(s):  
Fourier Series ◽  
Euclidean Space ◽  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Dimensional Euclidean Space ◽  
Vilenkin Groups ◽  
Lipschitz Conditions

In [4] we proved some theorems on the Fourier Transforms of functions satisfying conditions related to the Dini-Lipschitz conditions on then-dimensional Euclidean spaceRnand the torus groupTn. In this paper we extend those theorems for functions with Fourier series on Vilenkin groups.

scholarly journals Fourier transforms of spherical distributions on compact symmetric spaces

2011 ◽  
Vol 109 (1) ◽  
pp. 93 ◽  
Author(s):  
Gestur Ólafsson ◽  
Henrik Schlichtkrull
Keyword(s):  
Fourier Transform ◽  
Symmetric Spaces ◽  
Fourier Transforms ◽  
Type Theorem ◽  
Compact Type ◽  
Smooth Functions ◽  
Invariant Distributions ◽  
Compact Symmetric Spaces ◽  
The Fourier Transform ◽  
Small Support

In our previous articles [27] and [28] we studied Fourier series on a symmetric space $M=U/K$ of the compact type. In particular, we proved a Paley-Wiener type theorem for the smooth functions on $M$, which have sufficiently small support and are $K$-invariant, respectively $K$-finite. In this article we extend these results to $K$-invariant distributions on $M$. We show that the Fourier transform of a distribution, which is supported in a sufficiently small ball around the base point, extends to a holomorphic function of exponential type. We describe the image of the Fourier transform in the space of holomorphic functions. Finally, we characterize the singular support of a distribution in terms of its Fourier transform, and we use the Paley-Wiener theorem to characterize the distributions of small support, which are in the range of a given invariant differential operator. The extension from symmetric spaces of compact type to all compact symmetric spaces is sketched in an appendix.

scholarly journals A Hardy-Littlewood theorem for spherical Fourier transforms on symmetric spaces

1987 ◽  
Vol 71 (1) ◽  
pp. 104-122 ◽  
Author(s):  
Masaaki Eguchi ◽  
Keisaku Kumahara
Keyword(s):  
Symmetric Spaces ◽  
Fourier Transforms ◽  
Littlewood Theorem
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