A general form of Heisenberg–Pauli–Weyl uncertainty inequality for the Dunkl transform

DOI10.1080/10652469.2012.699966zbMath1270.42011OpenAlexW2039107049MaRDI QIDQ2841936

Fethi Soltani

Publication date: 30 July 2013

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2012.699966

zbMATH Keywords

Dunkl transformHeisenberg-Pauli-Weyl uncertainty principle

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10)

Related Items (21)

A variation of \(L^p\) uncertainty principles in Weinstein setting ⋮ Uncertainty principles for the Dunkl-Wigner transforms ⋮ New results on the continuous Weinstein wavelet transform ⋮ Time-frequency concentration, Heisenberg type uncertainty principles and localization operators for the continuous Dunkl wavelet transform on \(\mathbb {R}^{d}\) ⋮ The Hardy inequality and fractional Hardy inequality for the Dunkl Laplacian ⋮ Uncertainty principles for the Hankel-Stockwell transform ⋮ Pitt's inequality and logarithmic uncertainty principle for the Dunkl transform on \(\mathbb R\) ⋮ Linear canonical Hankel domain based Stockwell transform and associated Heisenberg's uncertainty principle ⋮ Tighter Heisenberg-Weyl type uncertainty principle associated with quaternion wavelet transform ⋮ Heisenberg uncertainty principles for the Dunkl multipier operators ⋮ Uncertainty principles and extremal functions for the Dunkl \(L^2\)-multiplier operators ⋮ Analytical and numerical approximation formulas on the Dunkl-type Fock spaces ⋮ Uncertainty principles for the Dunkl-type Segal-Bargmann transform ⋮ Pitt's inequalities for the Dunkl transform on ℝ^d ⋮ Unnamed Item ⋮ Inversion theorem and quantitative uncertainty principles for the Dunkl Gabor transform on \({\mathbb{R}}^d\) ⋮ Uncertainty principles for the continuous Hankel Wavelet transform ⋮ Uncertainty principles for the windowed Hankel transform ⋮ Hardy inequality and trace Hardy inequality for Dunkl gradient ⋮ A variety of uncertainty principles for the Dunkl transform on ℝd ⋮ Weighted norm inequalities for the Opdam–Cherednik transform

Cites Work

• Riesz transform and Riesz potentials for Dunkl transform
• Heisenberg-Pauli-Weyl uncertainty principle for the spherical mean operator
• Markov processes related with Dunkl operators
• The Dunkl transform
• The uncertainty principle: A mathematical survey
• Positivity of Dunkl's intertwining operator
• Heisenberg-Pauli-Weyl uncertainty inequalities and polynomial volume growth
• Convolution operator and maximal function for the Dunkl transform
• A Note on Entropy
• Integral Kernels with Reflection Group Invariance
• An uncertainty principle for the Dunkl transform
• A positive radial product formula for the Dunkl kernel
• Inversion formulas in the Dunkl-type heat conduction on

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