Results 101 to 110 of about 2,908 (161)

Oscillation inequalities for Carleson–Dunkl operator

Rendiconti del Circolo Matematico di Palermo Series 2
Abstract In this paper, we establish estimates for the oscillation seminorm for the so-called Carleson–Dunkl operator on weighted $$L^p(\mathbb {R},w(x)|x|^{2\alpha +1}\textrm{d}x)$$ L p
openaire   +2 more sources

Pitt's inequalities and uncertainty principle for generalized Fourier transform

, 2015
We study the two-parameter family of unitary operators \[ \mathcal{F}_{k,a}=\exp\Bigl(\frac{i\pi}{2a}\,(2\langle k\rangle+{d}+a-2 )\Bigr) \exp\Bigl(\frac{i\pi}{2a}\,\Delta_{k,a}\Bigr), \] which are called $(k,a)$-generalized Fourier transforms and ...
Gorbachev, Dmitry, Ivanov, Valery, Tikhonov, Sergey   +2 more
core  

Imaginary Powers of the Dunkl Harmonic Oscillator

Symmetry, Integrability and Geometry: Methods and Applications, 2009
In this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on Rd isomorphic to Z_2^d. We prove that imaginary powers of this operator are bounded on L^p, 1 < p < ∞, and from L^1
Adam Nowak, Krzysztof Stempak
doaj   +1 more source

Inversion of the Dunkl Intertwining Operator and Its Dual Using Dunkl Wavelets

Rocky Mountain Journal of Mathematics, 2002
In \S1 of the paper, the author gives results on the Dunkl operators and on eigenfunction called the Dunkl kernel and then he defines the Dunkl intertwining operator \(V_k\) and its dual \({}^tV_k\) and mentions their main properties. In Sections 3 and 4, the harmonic analysis associated with Dunkl operators (Dunkl transform, Dunkl translation ...
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The Diffusion Equation Involving the Dunkl–Laplacian Operator in a Punctured Domain

Fractal and Fractional
The purpose of this paper is to establish solvability results for both direct and inverse problems associated with the diffusion equation involving the Dunkl–Laplacian operator in a punctured domain.
Bayan Bekbolat, Gulzat Nalzhupbayeva, Niyaz Tokmagambetov   +2 more
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Dunkl analogue of Szász-mirakjan operators of blending type

Open Mathematics, 2018
In the present work, we construct a Dunkl generalization of the modified Szász-Mirakjan operators of integral form defined by Pǎltanea [1]. We study the approximation properties of these operators including weighted Korovkin theorem, the rate of ...
Deshwal Sheetal, Agrawal P.N., Araci Serkan   +2 more
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SHARP CONDITIONS FOR WEIGHTED INTEGRABILITY OF q-DUNKL FOURIER TRANSFORMS

Проблемы анализа
We obtain sufficient conditions for the weighted inte grability of the q-Dunkl Fourier transforms of functions from gen eralized integral Lipschitz classes. In the L^2 case, we prove the sharpness of these conditions.
S. S. Volosivets
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Hilbert Transforms Associated with Dunkl-Hermite Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2009
We consider expansions of functions in L^p(R,|x|^{2k}dx), 1 ≤ p < +∞ with respect to Dunkl-Hermite functions in the rank-one setting. We actually define the heat-diffusion and Poisson integrals in the one-dimensional Dunkl setting and study their ...
Néjib Ben Salem, Taha Samaali
doaj   +1 more source

A Dunkl type generalization of Szász operators via post-quantum calculus. [PDF]

J Inequal Appl, 2018
Alotaibi A, Nasiruzzaman M, Mursaleen M.
europepmc   +1 more source

A Hahn-Type Characterization of Generalized Hermite Polynomials Through a Dunkl-Based Raising Operator

Mathematics
In this paper, we study Hahn’s problem with respect to a Dunkl-perturbed raising operator. More precisely, we prove that, up to a dilation, the generalized Hermite polynomials are the only Tμ,α-classical symmetric orthogonal polynomials, where Tμ,α=Tμ ...
Khalid Ali Alanezy, Jihad Souissi
doaj   +1 more source