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We consider Fourier multipliers for Lp associated with the Dunkl operator on and establish a version of Hörmander's multiplier theorem. In applying this version, we come up with some results regarding the oscillating multipliers, partial sum operators and generalized Bessel potentials.  相似文献
2.
We use the Fourier analysis associated to a singular second-order differential operator Δ, and prove a continuous-time principle for the L p theory.  相似文献
3.
We give an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev spaces associated with a singular second-order differential operator. Next, we come up with some results regarding the multiplier operators for the Sturm–Liouville transform.  相似文献
4.
We study the dual Dunkl-Sonine operator tSk,? on ?d, and give expression of tSk,?, using Dunkl multiplier operators on ?d. Next, we study the extremal functions f*λ, λ >0 related to the Dunkl multiplier operators, and more precisely show that {f*λ} λ >0 converges uniformly to tSk,?(f) as λ → 0+. Certain examples based on Dunkl-heat and Dunkl-Poisson kernels are provided to illustrate the results.  相似文献
5.
We study some class of Dunkl multiplier operators; and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark''s uncertainty principle. For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.  相似文献
6.
We define and study the Fourier-Wigner transform associated with the Dunkl operators, and we prove for this transform an inversion formula. Next, we introduce and study the Weyl transforms $W_{\sigma}$ associated with the Dunkl operators, where $\sigma$ is a symbol in the Schwartz space $\mathcal{S}(\mathbb{R}^d\times\mathbb{R}^d)$. An integral relation between the precedent Weyl and Wigner transforms is given. At last, we give criteria in terms of $\sigma$ for boundedness and compactness of the transform $W_{\sigma}$.  相似文献
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8.
We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles: local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark''s uncertainty principle and Matolcsi-Sz\"ucs uncertainty principle.  相似文献
9.
We investigate the Dunkl transform Fk{\mathcal{F}_k} on Hardy type space in the Dunkl setting and establish a version of Paley type inequality for this transform.  相似文献
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