The Dunkl-Laplace transform and Macdonald's hypergeometric series
, 2022 We continue a program generalizing classical results from the analysis on symmetric cones to the Dunkl setting for root systems of type A. In particular, we prove a Dunkl-Laplace transform identity for Heckman-Opdam hypergeometric functions of type A and
Rösler, Margit, Brennecken, Dominik
core
Gabor Transform Associated with the Dunkl–Bessel Transform and Spectrograms
SymmetryTime–frequency (or space–phase) analysis plays a key role in signal analysis. In particular, signals that have a very concentrated time–frequency content are of great importance. However, the uncertainty principle sets a limitation to the possible simultaneous concentration of a function and its Dunkl–Bessel transform.
Saifallah Ghobber +2 more
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Dunkl convolution and elliptic regularity for Dunkl operators
Mathematische Nachrichten, Volume 297, Issue 12, Page 4416-4436, December 2024.Abstract We discuss in which cases the Dunkl convolution u∗kv$u*_kv$ of distributions u,v$u,v$, possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions.
Dominik Brennecken
wiley +1 more source
Uncertainty principles for the Dunkl transform
Hiroshima Mathematical Journal, 2010 The uncertainty principle for the classical Fourier transform was proved by many mathematicians including Hardy and Beurling and its \(L^p\) version was proved by Cowling and Price. The above results for the Fourier transform were generalized to the Dunkl transform by Gallardo, Trimèche.
Kawazoe, Takeshi, Mejjaoli, Hatem
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Uncertainty Inequalities for the Linear Canonical Dunkl Transform
MathematicsThe aim of this paper is to show some uncertainty inequalities for the linear canonical Dunkl transform (LCDT), including sharp Heisenberg-type, entropic-type, logarithmic-type, Donoho–Stark-type and local-type uncertainty principles.
Saifallah Ghobber, Hatem Mejjaoli
doaj +1 more source
Exact solutions of [Formula: see text]-dependent Schrödinger equation with quantum pseudo-harmonic oscillator and its applications for the thermodynamic properties in normal and superstatistics. [PDF]
Sci Rep, 2023 Okorie US +7 more
europepmc +1 more source
Reproducing kernels for Dunkl polyharmonic polynomials [PDF]
, 2012 summary:In this paper, we compute explicitly the reproducing kernel of the space of homogeneous polynomials of degree $n$ and Dunkl polyharmonic of degree $m$, i.e.
Touahri, Kamel
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Localization Operators for the Linear Canonical Dunkl Windowed Transformation
AxiomsOne of the best known time–frequency tools for examining non-transient signals is the linear canonical windowed transform, which has been used extensively in signal processing and related domains. In this paper, by involving the harmonic analysis for the
Saifallah Ghobber, Hatem Mejjaoli
doaj +1 more source
On Some Inequalities in Normed Linear Spaces [PDF]
, 2007 Upper and lower bounds for the norm of a linear combination of vectors are given. Applications in obtaining various inequalities for the quantities ||x/||x|| - y/||y|| || and ||x/||y|| - y/||x|| ||, where x and y are nonzero vectors, that are related ...
Dragomir, Sever S
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A New Wavelet Transform and Its Localization Operators
MathematicsIn the present paper we define and study a new wavelet transformation associated to the linear canonical Dunkl transform (LCDT), which has been widely used in signal processing and other related fields.
Saifallah Ghobber, Hatem Mejjaoli
doaj +1 more source