Generalized convolution operator associated with the \((k, a)\)-generalized Fourier transform on the real line and applications

DOI10.1007/s11785-023-01473-2OpenAlexW4391741750MaRDI QIDQ6196067

Hatem Mejjaoli

Publication date: 14 March 2024

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-023-01473-2

zbMATH Keywords

generalized convolution\((k, a)\)-generalized Fourier transform\((k, a)\)-generalized translation\((k, a)\)-generalized wavelet

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Integral operators (47G10) Pseudodifferential operators (47G30)

Cites Work

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• Explicit formulas for the Dunkl dihedral kernel and the \((\kappa,a)\)-generalized Fourier kernel
• Wavelet transforms and localization operators
• Polar wavelet transform and the associated uncertainty principles
• Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in \(L^2\)
• The continuous wavelet transform associated with a differential-difference operator and applications
• Spectral theorems associated with the \((k,a)\)-generalized wavelet multipliers
• A product formula and a convolution structure for a \(k\)-Hankel transform on \(\mathbb{R}\)
• A Hardy-Littlewood maximal operator for the generalized Fourier transform on \(\mathbb{R}\)
• \(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) and its applications to the reproducing kernel theory
• Time-frequency analysis associated with the \(k\)-Hankel Gabor transform on \(\mathbb{R}^d\)
• \(k\)-Hankel Wigner transform and its applications to the localization operators theory
• \((k,a)\)-generalized wavelet transform and applications
• Translation operator and maximal function for the \((k,1)\)-generalized Fourier transform
• Convolution operator and maximal function for the Dunkl transform
• Weighted inequalities and uncertainty principles for the (k,a)-generalized Fourier transform
• Wavelet Transforms and Their Applications
• On the Clifford-Fourier Transform
• Laguerre semigroup and Dunkl operators
• The $\mathfrak {su}(2)_\alpha $ Hahn oscillator and a discrete Fourier–Hahn transform
• Multivariable Bessel Gabor transform and applications
• Differential-Difference Operators Associated to Reflection Groups
• Clifford algebras, Fourier transforms, and quantum mechanics
• The Hausdorff operator is bounded on the real Hardy space 𝐻¹(ℝ)
• A new product formula involving Bessel functions
• New uncertainty principles for the $(k,a)$-generalized wavelet transform
• k-Hankel two-wavelet theory and localization operators
• Localization Operators and Uncertainty Principles for the Hankel Wavelet Transform
• Some results on wavelet scalograms
• Lecture Notes on Wavelet Transforms
• Uncertainty principles for the continuous wavelet transform in the Hankel setting
• L p -L q Boundedness of (k, a)-Fourier Multipliers with Applications to Nonlinear Equations
• Flett potentials associated with differential-difference Laplace operators
• Norm inequalities for maximal operators
• Generalized translation operator and uncertainty principles associated with the deformed Stockwell transform

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