Displaying similar documents to “Inversion formulas for the Dunkl intertwining operator and its dual on spaces of functions and distributions.”

Spectrum of Functions for the Dunkl Transform on R^d

Mejjaoli, Hatem, Trimèche, Khalifa (2007)

Fractional Calculus and Applied Analysis

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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.

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

Abdelkefi, Chokri, Sifi, Mohamed (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 44A15, 44A35, 46E30 In this paper we prove that the partial Dunkl integral ST(f) of f converges to f, as T → +∞ in L^∞(νµ) and we show that the Dunkl transform Fµ(f) of f is in L^1(νµ) when f belongs to a suitable Besov-Dunkl space. We also give sufficient conditions on a function f in order that the Dunkl transform Fµ(f) of f is in a L^p -space. * Supported by 04/UR/15-02.

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mejjaoli, Hatem (2006)

Fractional Calculus and Applied Analysis

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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.

Between the Paley-Wiener theorem and the Bochner tube theorem

Zofia Szmydt, Bogdan Ziemian (1995)

Annales Polonici Mathematici

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We present the classical Paley-Wiener-Schwartz theorem [1] on the Laplace transform of a compactly supported distribution in a new framework which arises naturally in the study of the Mellin transformation. In particular, sufficient conditions for a function to be the Mellin (Laplace) transform of a compactly supported distribution are given in the form resembling the Bochner tube theorem [2].

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

Kamoun, Lotfi (2005)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 42B10, 43A32. In this paper we take the strip KL = [0, +∞[×[−Lπ, Lπ], where L is a positive integer. We consider, for a nonnegative real number α, two partial differential operators D and Dα on ]0, +∞[×] − Lπ, Lπ[. We associate a generalized Fourier transform Fα to the operators D and Dα. For this transform Fα, we establish an Lp − Lq − version of the Morgan's theorem under the assumption 1 ≤ p, q ≤ +∞.

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

Gasmi, A., Sifi, M., Soltani, F. (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35 We introduce some new weighted Herz spaces associated with the Dunkl operator on R. Also we characterize by atomic decompositions the corresponding Herz-type Hardy spaces. As applications we investigate the Dunkl transform on these spaces and establish a version of Hardy inequality for this transform. * The authors are supported by the DGRST research project 04/UR/15-02.

On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin

Südland, Norbert, Baumann, Gerd (2004)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 44A05, 46F12, 28A78 We prove that Dirac’s (symmetrical) delta function and the Hausdorff dimension function build up a pair of reciprocal functions. Our reasoning is based on the theorem by Mellin. Applications of the reciprocity relation demonstrate the merit of this approach.