共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we define the Hankel–Wigner transform in Clifford analysis and therefore define the corresponding Weyl transform. We present some properties of this kind of Hankel–Wigner transform, and then give the criteria of the boundedness of the Weyl transform and compactness on the Lp space. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
2.
3.
Kanailal Mahato 《Integral Transforms and Special Functions》2017,28(11):789-800
This article is concerned with the study of the continuity of wavelet transform involving fractional Hankel transform on certain function spaces. The n-dimensional boundedness property of the fractional wavelet transform is also discussed on Sobolev type space. Particular cases are also considered. 相似文献
4.
Using the theory of Hankel convolution, continuous and discrete Bessel wavelet transforms are defined. Certain boundedness results and inversion formula for the continuous Bessel wavelet transform are obtained. Important properties of the discrete Bessel wavelet transform are given. 相似文献
5.
6.
7.
C. Baccar 《Integral Transforms and Special Functions》2016,27(6):413-429
The aim of this paper is to prove Heisenberg-type uncertainty principles for the continuous Hankel wavelet transform. We also analyse the concentration of this transform on sets of finite measure. Benedicks-type uncertainty principle is given. 相似文献
8.
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
9.
An uncertainty principle for Hankel transforms 总被引:1,自引:0,他引:1
Margit Rö sler Michael Voit 《Proceedings of the American Mathematical Society》1999,127(1):183-194
There exists a generalized Hankel transform of order on , which is based on the eigenfunctions of the Dunkl operator
For this transform coincides with the usual Fourier transform on . In this paper the operator replaces the usual first derivative in order to obtain a sharp uncertainty principle for generalized Hankel transforms on . It generalizes the classical Weyl-Heisenberg uncertainty principle for the position and momentum operators on ; moreover, it implies a Weyl-Heisenberg inequality for the classical Hankel transform of arbitrary order on
10.
On the Sobolev boundedness results of the product of pseudo-differential operators involving a couple of fractional Hankel transforms
下载免费PDF全文
![点击此处可从《数学学报(英文版)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed. 相似文献
11.
The main goal of this paper is to study about the continuous as well as discrete wavelet transform in terms of linear canonical Hankel transform (LCH‐transform) and discuss some of its basic properties. Parseval's relation and reconstruction formula of continuous linear canonical Hankel wavelet transform (CLCH‐wavelet transform) is obtained. Moreover, semidiscrete and discrete LCH‐wavelet transform are also discussed. 相似文献
12.
In this present article, we study the fractional Hankel transform and its inverse on certain Gel'fand‐Shilov spaces of type S. The continuous fractional wavelet transform is defined involving the fractional Hankel transform. The continuity of fractional Hankel wavelet transform is discussed on Gel'fand‐Shilov spaces of type S. This article goes further to discuss the continuity property of fractional Hankel transform and fractional Hankel wavelet transform on the ultradifferentiable function spaces. 相似文献
13.
Shapiro’s dispersion and Umbrella theorems are proved for the continuous Hankel wavelet transform. As a side results, we extend local uncertainty principles for set of finite measure to the latter transform. 相似文献
14.
Abderrazek Karoui Taher Moumni 《Journal of Computational and Applied Mathematics》2009,233(2):315-333
In this paper, we develop two practical methods for the computation of the eigenvalues as well as the eigenfunctions of the finite Hankel transform operator. These different eigenfunctions are called circular prolate spheroidal wave functions (CPSWFs). This work is motivated by the potential applications of the CPSWFs as well as the development of practical methods for computing their values. Also, in this work, we should prove that the CPSWFs form an orthonormal basis of the space of Hankel band-limited functions, an orthogonal basis of L2([0,1]) and an orthonormal system of L2([0,+∞[). Our computation of the CPSWFs and their associated eigenvalues is done by the use of two different methods. The first method is based on a suitable matrix representation of the finite Hankel transform operator. The second method is based on the use of an efficient quadrature method based on a special family of orthogonal polynomials. Also, we give two Maple programs that implement the previous two methods. Finally, we present some numerical results that illustrate the results of this work. 相似文献
15.
在这篇文章里,我们研究了Weyl-Heisenberg前框架的性质。结果,我们得到了它的若干新特性。 相似文献
16.
Radica Bojičić Marko D. Petković Predrag M. Rajković 《Mathematical Methods in the Applied Sciences》2017,40(16):5810-5820
We study Hankel transform of the sequences (u,l,d),t, and the classical Motzkin numbers. Using the method based on orthogonal polynomials, we give closed‐form evaluations of the Hankel transform of the aforementioned sequences, sums of two consecutive, and shifted sequences. We also show that these sequences satisfy some interesting convolutional properties. Finally, we partially consider the Hankel transform evaluation of the sums of two consecutive shifted (u,l,d)‐Motzkin numbers. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
17.
18.
Sandeep Kumar Verma Akhilesh Prasad 《Mathematical Methods in the Applied Sciences》2020,43(15):9119-9128
In this paper, we define the windowed-Mehler–Fock transform and introduce the corresponding Weyl transform. Further, we examine the boundedness of windowed-Mehler–Fock transform in Lebesgue space and establish some of its fundamental properties. Also, we give the criteria of boundedness and compactness of Weyl transform in Lebesgue space. 相似文献
19.
考虑Simon反谱理论新方法中引入的A-函数,根据Weyl函数m关于A-函数的表示关系,利用广义函数和Fourier变换的方法求出A-函数关于Weyl函数m的反表示,该结论表明A-函数的本质是广义函数. 相似文献
20.
We prove Pitt and Boas inequalities for products of radial functions and spherical harmonics in Rn. In the process, we obtain upper and lower estimates of the operator norm of the Hankel transform with power weights. Our inequalities are sharp in some specific cases. 相似文献