共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we consider the Dunkl operators T
j
, j = 1, . . . , d, on and the harmonic analysis associated with these operators. We define a continuous Dunkl Gabor transform, involving the Dunkl
translation operator, by proceeding as mentioned in [20] by C.Wojciech and G. Gigante. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. Then, we show that the portion of the continuous Dunkl Gabor transform
lying outside some set of finite measure cannot be arbitrarily too small. Similarly, using the basic theory for the Dunkl
continuous wavelet transform introduced by K. Trimèche in [18], an analogous of this result for the Dunkl continuous wavelet
transform is given. Finally, an analogous of Heisenberg’s inequality for a continuous Dunkl Gabor transform (resp. Dunkl continuous
wavelet transform) is proved.
相似文献
2.
Hatem Mejjaoli 《Applicable analysis》2013,92(9):1980-2007
In this article we characterize the Dunkl–Besov spaces and prove the embedding Sobolev theorems via the Dunkl heat semigroup. We also study the dispersive properties of the solutions of the Dunkl heat equation. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems on generalized functional spaces. 相似文献
3.
By expressing the Dunkl transform of order α of a function f in terms of the Hankel transforms of orders α and α + 1 of even and odd parts of f, respectively, we show that a considerable part of harmonic analysis of the Dunkl transform on the real line may be reduced to known results for the Hankel transform. In particular, defining the modified Dunkl transform and then considering the Dunkl transplantation operator we transfer known multiplier results for the Hankel transform to the Dunkl transform setting. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
M. Maslouhi 《Journal of Functional Analysis》2009,256(8):2697-2864
We consider Dunkl theory associated to a general Coxeter group G. A new characterization of the regularity of the weight k is given and a new construction, devoid of Kozul complex theory, of the Dunkl intertwining operator Vk is established. We apply our results to derive sharp estimates of the Dunkl kernel. We give explicit formula in the case of orthogonal positive root systems. 相似文献
5.
In this paper we give a necessary and sufficient condition in terms of the Jacobi–Dunkl transform in order that a Jacobi–Dunkl
convolution of distributions is hypoelliptic. 相似文献
6.
Chokri Abdelkefi 《Mediterranean Journal of Mathematics》2012,9(3):499-513
We introduce first weighted function spaces on ${\mathbb{R}^d}$ using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on ${\mathbb{R}^d}$ weighted L p -estimates of the Dunkl transform of a function in terms of an integral modulus of continuity which gives a quantitative form of the Riemann-Lebesgue lemma. Finally, we show in both cases that the Dunkl transform of a function is in L 1 when this function belongs to a suitable Besov-Dunkl space. 相似文献
7.
REN Guangbin Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2005,48(Z1)
Let Ωbe a G-invariant convex domain in RN including 0, where G is a Coxeter group associated with reduced root system R. We consider functions f defined in Ωwhich are Dunkl polyharmonic, i.e. (△h)nf =0 for some integer n. Here △h=∑j=1N Dj2 is the Dunkl Laplacian, and Dj is the Dunkl operator attached to the Coxeter group G, where kv is a multiplicity function on R and σv is the reflection with respect to the root v. We prove that any Dunkl polyharmonic function f has a decomposition of the form f(x)=f0(x) |x|2f1(x) … |x|2(n-1)fn-1(x),(?)x∈Ω, where fj are Dunkl harmonic functions, i.e. △hfj = 0. This generalizes the classical Almansi theorem for polyharmonic functions as well as the Fischer decomposition. 相似文献
8.
Let Ω be a G-invariant convex domain in ℝN including 0, where G is a Coxeter group associated with reduced root system R. We consider functions f defined in Ω which are Dunkl polyharmonic, i.e. (Δh)nf = 0 for some integer n. Here333-01is the Dunkl Laplacian, and Dj is the Dunkl operator attached to the Coxeter group G,
$$\mathcal{D}_j f(x) = \frac{\partial }{{\partial x_j }}f(x) + \sum\limits_{v \in R_ + } {\kappa _v \frac{{f(x) - f(\sigma _v x)}}{{\left\langle {x,v} \right\rangle }}} v_j ,$$where Kv is a multiplicity function on R and σv is the reflection with respect to the root v. We prove that any Dunkl polyharmonic function f has a decomposition of the form
$$f(x) = f_0 (x) + \left| x \right|^2 f_1 (x) + \cdots + \left| x \right|^{2(n - 1)} f_{n - 1} (x), \forall x \in \Omega ,$$where fj are Dunkl harmonic functions, i.e. Δhfj = 0. This generalizes the classical Almansi theorem for polyharmonic functions as well as the Fischer decomposition.
相似文献9.
10.
Dunkl operators are parameterized differential-difference operators on
Nthat are related to finite reflection groups. They can be regarded as a generalization of partial derivatives and play a major role in the study of Calogero–Moser–Sutherland-type quantum many-body systems. Dunkl operators lead to generalizations of various analytic structures, like the Laplace operator, the Fourier transform, Hermite polynomials, and the heat semigroup. In this paper we investigate some probabilistic aspects of this theory in a systematic way. For this, we introduce a concept of homogeneity of Markov processes on
Nthat generalizes the classical notion of processes with independent, stationary increments to the Dunkl setting. This includes analogues of Brownian motion and Cauchy processes. The generalizations of Brownian motion have the càdlàg property and form, after symmetrization with respect to the underlying reflection groups, diffusions on the Weyl chambers. A major part of the paper is devoted to the concept of modified moments of probability measures on
Nin the Dunkl setting. This leads to several results for homogeneous Markov processes (in our extended setting), including martingale characterizations and limit theorems. Furthermore, relations to generalized Hermite polynomials, Appell systems, and Ornstein–Uhlenbeck processes are discussed. 相似文献
11.
We study an extension of the classical Paley–Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier–Neumann type series as special cases, and it also provides a bilinear expansion for the Dunkl kernel (in the rank 1 case) which is a Dunkl analogue of Gegenbauer’s expansion of the plane wave and the corresponding sampling expansions. In fact, we show how to derive sampling and Fourier–Neumann type expansions from the results related to the bilinear expansion for the Dunkl kernel. 相似文献
12.
GuangBin Ren 《中国科学 数学(英文版)》2010,53(12):3153-3162
In the framework of superspace in Clifford analysis for the Dunkl version, the Fischer decomposition is established for solutions of the Dunkl super Dirac operators. The result is general without restrictions on multiplicity functions or on super dimensions. The Fischer decomposition provides a module for the Howe dual pair G × osp(1|2) on the space of spinor valued polynomials with G the Coxeter group, while the generators of the Lie superspace reveal the naturality of the Fischer decomposition. 相似文献
13.
In this paper we study a class of generalized Fock spaces associated with the Dunkl operator. Next we introduce the commutator relations between the Dunkl operator and multiplication operator which leads to a generalized class of Weyl relations for the Dunkl kernel. 相似文献
14.
Fethi Soltani 《Archiv der Mathematik》2010,95(1):35-44
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
15.
For a family of weight functions invariant under a finite reflection group, we show how weighted Lp multiplier theorems for Dunkl transform on the Euclidean space Rd can be transferred from the corresponding results for h-harmonic expansions on the unit sphere Sd of Rd+1. The result is then applied to establish a Hörmander type multiplier theorem for the Dunkl transform and to show the convergence of the Bochner-Riesz means of the Dunkl transform of order above the critical index in weighted Lp spaces. 相似文献
16.
Mathematical Notes - We define a fractional power of the Dunkl Laplacian, a fractional modulus of smoothness, and a fractional K-functional on Lp-spaces with Dunkl weight. As an application, we... 相似文献
17.
Chokri Yacoub 《Advances in Applied Clifford Algebras》2011,21(4):839-847
In this note, Kelvin transform is introduced in the framework of Dunkl-Clifford analysis. It is shown that this transform
preserves the class of Dunkl monogenic functions. As an application, we use it to generate Dunkl monogenic polynomials by
a classical process due to Maxwell. 相似文献
18.
For a family of weight functionsh
K invariant under a finite reflection group onR
d, analysis related to the Dunkl transform is carried out for the weightedL
p spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the
inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a maximal
function and use it to prove the almost everywhere convergence.
ST wishes to thank YX for the warm hospitality during his stay in Eugene. The work of YX was supported in part by the National
Science Foundation under Grant DMS-0201669. 相似文献
19.
Khalifa Trimèche 《Journal of Fourier Analysis and Applications》2006,12(5):517-542
In this article we define and study the Dunkl convolution product and the Dunkl transform on spaces of distributions on
By using the main results obtained, we study the hypoelliptic Dunkl convolution equations in the space of distributions. 相似文献
20.
The main purpose of this article is to study the L
p
-boundedness of linear and bilinear multiplier operators for the Dunkl transform in the one dimensional case. 相似文献