AN ANALOGUE OF COWLING–PRICE'S THEOREM AND HARDY'S THEOREM FOR THE GENERALIZED FOURIER TRANSFORM ASSOCIATED WITH THE SPHERICAL MEAN OPERATOR

2004 ◽  
Vol 02 (03) ◽  
pp. 177-192 ◽  
Author(s):  
C. CHETTAOUI ◽  
Y. OTHMANI ◽  
K. TRIMÈCHE
Keyword(s):  
Fourier Transform ◽  
Harmonic Analysis ◽  
Generalized Fourier Transform ◽  
Spherical Mean Operator ◽  
Hardy’S Theorem ◽  
Spherical Mean

Using the harmonic analysis associated with the spherical mean operator R and its dualtR we establish an analogue of Cowling–Price's theorem and Hardy's theorem for the spherical mean operator R.

scholarly journals Spaces ofDLptype and a convolution product associated with the spherical mean operator

2005 ◽  
Vol 2005 (3) ◽  
pp. 357-381 ◽  
Author(s):  
M. Dziri ◽  
M. Jelassi ◽  
L. T. Rachdi
Keyword(s):  
Harmonic Analysis ◽  
Dual Space ◽  
Convolution Product ◽  
Spherical Mean Operator ◽  
Spherical Mean

We define and study the spacesℳp(ℝ×ℝn),1≤p≤∞, that are ofDLptype. Using the harmonic analysis associated with the spherical mean operator, we give a new characterization of the dual spaceℳ′p(ℝ×ℝn)and describe its bounded subsets. Next, we define a convolution product inℳ′p(ℝ×ℝn)×Mr(ℝ×ℝn),1≤r≤p<∞, and prove some new results.

Uncertainty principle related to Flensted–Jensen partial differential operators

2019 ◽  
pp. 2150004
Author(s):  
Raoudha Laffi ◽  
Selma Negzaoui
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Differential Operators ◽  
Generalized Fourier Transform ◽  
Partial Differential ◽  
Hardy’S Theorem ◽  
Partial Differential Operators ◽  
Hörmander's Theorem

This paper deals with some formulations of the uncertainty principle associated to generalized Fourier transform [Formula: see text] related to Flensted–Jensen partial differential operators. The aim result is to prove the analogue of Bonami–Demange–Jaming’s theorem : A version of Beurling–Hörmander’s theorem which gives more precision in the form of nonzero functions verifying modified-Beurling’s condition. As application, we get analogous of Gelfand–Schilov’s theorem, Cowling–Price’s theorem and Hardy’s theorem for [Formula: see text].

scholarly journals Direct and inverse theorems of approximation theory

MATEMATIKA ◽  
2017 ◽  
Vol 33 (2) ◽  
pp. 177
Author(s):  
Radouan Daher ◽  
Salah El Ouadih ◽  
Mohamed El Hamma
Keyword(s):  
Harmonic Analysis ◽  
Approximation Theory ◽  
Spherical Mean Operator ◽  
Spherical Mean ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems ◽  
Generalized Spherical Mean Operator

In this paper, we prove analogues of direct and some inverse theorems, for the Dunkl harmonic analysis, using the function with bounded spectrum and generalized spherical mean operator.

WEYL TRANSFORMS ASSOCIATED WITH THE SPHERICAL MEAN OPERATOR

2003 ◽  
Vol 01 (02) ◽  
pp. 141-164 ◽  
Author(s):  
L. T. RACHDI ◽  
K. TRIMÈCHE
Keyword(s):  
Harmonic Analysis ◽  
Spherical Mean Operator ◽  
Weyl Transforms ◽  
Spherical Mean

Using the harmonic analysis associated with the spherical mean operator ℛ, we define and study the Weyl transforms Wσ associated with ℛ where σ is a symbol in Sm, m ∈ ℝ, and we give criteria in terms of σ to obtain the boundedness and compactness of the transform Wσ.

scholarly journals A generalized Fourier transform approach to risk measures

2010 ◽  
Vol 2010 (01) ◽  
pp. P01005 ◽  
Author(s):  
Giacomo Bormetti ◽  
Valentina Cazzola ◽  
Giacomo Livan ◽  
Guido Montagna ◽  
Oreste Nicrosini
Keyword(s):  
Fourier Transform ◽  
Risk Measures ◽  
Generalized Fourier Transform
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