A few results about the -Laplace's operator.
Covei, Dragoş-Pătru (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
Similarity:
Covei, Dragoş-Pătru (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
Similarity:
Zofia Szmydt, Bogdan Ziemian (1995)
Annales Polonici Mathematici
Similarity:
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].
Südland, Norbert, Baumann, Gerd (2004)
Fractional Calculus and Applied Analysis
Similarity:
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.
Mejjaoli, Hatem (2006)
Fractional Calculus and Applied Analysis
Similarity:
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.
B. Stanković (2004)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Similarity:
B. Stanković (2002)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Similarity:
Mejjaoli, Hatem, Trimèche, Khalifa (2007)
Fractional Calculus and Applied Analysis
Similarity:
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.
Babakhani, Ali, Dahiya, R.S. (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Similarity:
Kamoun, Lotfi (2005)
Fractional Calculus and Applied Analysis
Similarity:
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 ≤ +∞.
Trimèche, Khalifa (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Similarity:
Abdelkefi, Chokri, Sifi, Mohamed (2006)
Fractional Calculus and Applied Analysis
Similarity:
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.