Positive -Bounded Dunkl-Type Generalized Translation Operator and Its Applications
DV Gorbachev, VI Ivanov, SY Tikhonov - Constructive approximation, 2019 - Springer
We prove that the spherical mean value of the Dunkl-type generalized translation operator
τ^ y τ y is a positive L^ p L p-bounded generalized translation operator T^ t T t. As …
τ^ y τ y is a positive L^ p L p-bounded generalized translation operator T^ t T t. As …
A new product formula involving Bessel functions
In this paper, we consider the normalized Bessel function of index α>− 1 2, we find an
integral representation of the term xnj α+ n (x) j α (y). This allows us to establish a product …
integral representation of the term xnj α+ n (x) j α (y). This allows us to establish a product …
Translation operator and maximal function for the (k, 1)-generalized Fourier transform
SB Saïd, L Deleaval - Journal of Functional Analysis, 2020 - Elsevier
In this paper we study a translation operator associated with the n-dimensional (k, 1)-
generalized Fourier transform, where k is a multiplicity function for the Dunkl operators. In …
generalized Fourier transform, where k is a multiplicity function for the Dunkl operators. In …
[HTML][HTML] Explicit formulas for the Dunkl dihedral kernel and the (κ, a)-generalized Fourier kernel
D Constales, H De Bie, P Lian - Journal of Mathematical Analysis and …, 2018 - Elsevier
In this paper, a new method is developed to obtain explicit and integral expressions for the
kernel of the (κ, a)-generalized Fourier transform for κ= 0. In the case of dihedral groups, this …
kernel of the (κ, a)-generalized Fourier transform for κ= 0. In the case of dihedral groups, this …
L p -Lq Boundedness of (k, a)-Fourier Multipliers with Applications to Nonlinear Equations
V Kumar, M Ruzhansky - International Mathematics Research …, 2023 - academic.oup.com
The-generalised Fourier transform is the unitary operator defined using the-deformed Dunkl
harmonic oscillator. The main aim of this paper is to prove-boundedness of-generalised …
harmonic oscillator. The main aim of this paper is to prove-boundedness of-generalised …
k-Hankel two-wavelet theory and localization operators
H Mejjaoli, K Trimèche - Integral Transforms and Special Functions, 2020 - Taylor & Francis
In this paper, we present the basic k-Hankel wavelet theory. Next, we study the
boundedness and compactness of localization operators associated with k-Hankel wavelet …
boundedness and compactness of localization operators associated with k-Hankel wavelet …
On the kernel of the-Generalized fourier transform
D Gorbachev, V Ivanov, S Tikhonov - Forum of Mathematics, Sigma, 2023 - cambridge.org
Abstract For the kernel $ B_ {\kappa, a}(x, y) $ of the $(\kappa, a) $-generalized Fourier
transform $\mathcal {F} _ {\kappa, a} $, acting in $ L^{2}(\mathbb {R}^{d}) $ with the weight …
transform $\mathcal {F} _ {\kappa, a} $, acting in $ L^{2}(\mathbb {R}^{d}) $ with the weight …
Quantitative Uncertainty Principles Associated with the k-Generalized Stockwell Transform
H Mejjaoli, K Trimèche - Mediterranean Journal of Mathematics, 2022 - Springer
In this paper, we introduce the k-generalized Stockwell transform on R. We investigate for
this transform the main theorems of Harmonic analysis as Plancherel's, Calderón's, and …
this transform the main theorems of Harmonic analysis as Plancherel's, Calderón's, and …
Norm inequalities for maximal operators
S Ben Said, S Negzaoui - Journal of Inequalities and Applications, 2022 - Springer
In this paper, we introduce a family of one-dimensional maximal operators M κ, m, κ≥ 0 and
m∈ N∖{0}, which includes the Hardy–Littlewood maximal operator as a special case (κ= 0 …
m∈ N∖{0}, which includes the Hardy–Littlewood maximal operator as a special case (κ= 0 …
[HTML][HTML] A product formula and a convolution structure for a k-Hankel transform on R
SB Saïd - Journal of Mathematical Analysis and Applications, 2018 - Elsevier
A product formula and a convolution structure for a k-Hankel transform on R - ScienceDirect Skip
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