$q$-Analogue of the Dunkl transform on the real line
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Publication:5193014
zbMath1179.33020arXiv0801.0069MaRDI QIDQ5193014
Rym H. Bettaieb, Néji Bettaibi
Publication date: 10 August 2009
Full work available at URL: https://arxiv.org/abs/0801.0069
Special integral transforms (Legendre, Hilbert, etc.) (44A15) Integral transforms of special functions (44A20) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Discrete version of topics in analysis (39A12)
Related Items (8)
On Nash and Carlson's inequalities for symmetric \(q\)-integral transforms ⋮ An analog of Titchmarsh's theorem for the q-Dunkl transform in the space \(L_{q,\alpha }^2({\mathbb{R}}_q)\) ⋮ Modulus of smoothness and theorems concerning approximation in the space \(L^2_{q,\alpha}(\mathbb{R}_q)\) with power weight ⋮ On the Jackson-type inequalities in approximation theory connected to the \(q\)-Dunkl operators in the weighted space \(L^2_{q, \alpha }(\mathbb{R}_q, |x|^{2 \alpha +1}d_q x )\) ⋮ Generalized discrete \(q\)-Hermite I polynomials and \(q\)-deformed oscillator ⋮ Growth properties of the \(q\)-Dunkl transform in the space \(L^p_{q,\alpha }({\mathbb{R}}_q,|x|^{2\alpha +1}d_qx)\) ⋮ On the generalized Hilbert transform and weighted Hardy spaces in \(q\)-Dunkl harmonic analysis ⋮ Characterizations of the symmetric \(T_{(\theta, q)}\)-classical orthogonal \(q\)-polynomials
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