Littlewood-paley decomposition associated with the dunkl operators and paraproduct operators.
Generalized Dunkl--Sobolev spaces of exponential type and applications.
Dunkl hyperbolic equations.
An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform
Mathematics Subject Classification: Primary 35R10, Secondary 44A15 We establish an analogue of Beurling-Hörmander’s theorem for the Dunkl-Bessel transform FD,B on R(d+1,+). We deduce an analogue of Gelfand-Shilov, Hardy, Cowling-Price and Morgan theorems on R(d+1,+) by using the heat kernel associated to the Dunkl-Bessel-Laplace operator.
Generalized homogeneous Besov spaces and their applications
2010 Mathematics Subject Classification: Primary 35L05. Secondary 46E35, 35J25, 22E30. In this paper we define the homogeneous Besov spaces associated with the Dunkl operators on R^d, and we give a complete analysis on these spaces and same applications.
Dunkl-Schrödinger Equations with and without Quadratic Potentials
2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10. The purpose of this paper is to study the dispersive properties of the solutions of the Dunkl-Schrödinger equation and their perturbations with potential. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems.
Spectrum of Functions for the Dunkl Transform on R^d
Mathematics Subject Classification: 42B10 In this paper, we establish real Paley-Wiener theorems for the Dunkl transform on R^d. More precisely, we characterize the functions in the Schwartz space S(R^d) and in L^2k(R^d) whose Dunkl transform has bounded, unbounded, convex and nonconvex support.
The linear symmetric systems associated with the modified Cherednik operators and applications
We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.
Uncertainty principles for the Weinstein transform
The Weinstein transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization and a variant of Cowling-Price theorem, Miyachi's theorem, Beurling's theorem, and Donoho-Stark's uncertainty principle are obtained for the Weinstein transform.
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