Qualitative uncertainty principles for the generalized Fourier transform associated to a Dunkl type operator on the real line

DOI10.1007/s13324-015-0111-7zbMath1352.43006OpenAlexW1709950784MaRDI QIDQ300509

Hatem Mejjaoli, Khalifa Trimèche

Publication date: 28 June 2016

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13324-015-0111-7

zbMATH Keywords

Beurling's theoremCowling-Price's theoremgeneralized Fourier transformHardy's type theoremMiyachi's theoremMorgan's theorem

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Other transforms and operators of Fourier type (43A32) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Reflection groups, reflection geometries (51F15)

Related Items (6)

Time-frequency analysis associated with the deformed Stockwell transform ⋮ Localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces ⋮ Qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces ⋮ Uncertainty principles for the windowed Opdam–Cherednik transform ⋮ Uncertainty principles for the Opdam–Cherednik transform on modulation spaces ⋮ Time-frequency analysis associated with the \(k\)-Hankel Gabor transform on \(\mathbb{R}^d\)

Cites Work

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• Inversion of the Lions transmutation operators using generalized wavelets
• Convolution structure associated with the Jacobi-Dunkl operator on \(\mathbb R\)
• Heat ``polynomials for a singular differential operator on (0,\(\infty)\)
• Beurling's theorem and \(L^p-L^q\) Morgan's theorem for step two nilpotent Lie groups
• Hardy and Cowling-price theorems associated with a Dunkl type differential-difference operator on the real line
• A generalization of Miyachi's theorem
• On Fourier transforms of functions supported on sets of finite Lebesgue measure
• The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer
• A uniqueness theorem of Beurling for Fourier transform pairs
• The Dunkl transform
• Uncertainty principle and \(L^{p}\)--\(L^{q}\)-sufficient pairs on noncompact real symmetric spaces
• Hermite functions and uncertainty principles for the Fourier and the windowed Fourier trans\-forms.
• Sobolev spaces associated with a Dunkl type differential-difference operator on the real line and applications
• The transmutation operators relating to a Dunkl type operator on \(\mathbb{R}\) and their positivity
• Uncertainty Principles and Signal Recovery
• Integral Kernels with Reflection Group Invariance
• TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A SINGULAR DIFFERENTIAL-DIFFERENCE OPERATOR ON THE REAL LINE
• POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON ${\mathbb R}$
• An L^P version of Hardy's theorem for the Dunkl transform
• A Theorem Concerning Fourier Transforms
• A Note on Fourier Transforms
• Uncertainty principles for integral operators
• AnL^p−L^q-version of Morgan's theorem for the Dunkl–Bessel transform
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions

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