Continuity of the fractional Hankel wavelet transform on the spaces of type S

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.     

Wavelet transform associated with linear canonical Hankel transform

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.     

Relating transplantation and multipliers for Dunkl and Hankel transforms

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)     

傅立叶变换与小波变换的比较教学

本文针对小波变换教学中小流变换概念理解困难的问题，提出了一种比较教学方法，通过分析小波变换与傅立叶变换之间的联系，并从四个方面进行对比，清楚地描述了小波变换的本质，从而对加深对小波变换的理解。     

Weyl transforms associated with the Hankel transform in Clifford analysis

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 L^p space. Copyright © 2005 John Wiley & Sons, Ltd.     

Dirichlet空间上Toeplitz算子与Berezin型变换相关的一些性质

本文研究了单位圆盘D 的Dirichlet 空间上Toeplitz 算子和小Hankel 算子. 利用Berezin 型变换讨论了Toeplitz 算子的不变子空间问题, 具有Berezin 型符号的Toeplitz 算子的渐进可乘性以及Toeplitz 算子的Riccati 方程的可解性. 应用Berezin 变换得到了Toeplitz 算子和小Hankel 算子可逆的充分条件. 此外, 还利用Hankel 算子和Berezin 变换刻画了算子2T_uv-T_uT_v-T_vT_u 的紧性, 其中函数u,v ∈ L^2,1.     

Uncertainty principles for the continuous Hankel Wavelet transform

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.     

Continuous and discrete Bessel wavelet transforms

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.     

Radial Multiresolution, Cuntz Algebras Representations and an Application to Fractals

We study Bernoulli type convolution measures on attractor sets arising from iterated function systems on R. In particular we examine orthogonality for Hankel frequencies in the Hilbert space of square integrable functions on the attractor coming from a radial multiresolution analysis on R³. A class of fractals emerges from a finite system of contractive affine mappings on the zeros of Bessel functions. We have then fractal measures on one hand and the geometry of radial wavelets on the other hand. More generally, multiresolutions serve as an operator theoretic framework for the study of such selfsimilar structures as wavelets, fractals, and recursive basis algorithms. The purpose of the present paper is to show that this can be done for a certain Bessel–Hankel transform. Submitted: February 20, 2008., Accepted: March 6, 2008.     

Uncertainty principles for the continuous wavelet transform in the Hankel setting

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.     

On the boundedness result of wavelet transform associated with fractional Hankel transform

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.     

再生核与小波变换

在再生核基本理论的基础上,介绍了再生核在小波变换中的作用,并且根据连续小波变换像空间是再生核Hilbert空间这一基本事实,借助再生核理论的特殊技巧,建立了Littlewood-Paley和Haar小波变换像空间的再生核函数与已知再生核空间的再生核的关系,为小波变换像空间的进一步研究提供理论基础.     

SMALL HANKEL OPERATORS ON WEIGHTEDBERGMAN SPACES OF BOUNDED SYMMETRIC DOMAINS

1IntroductionLetnbeaboundedsynunetricdomaininC"withBerg1llankernelK(z,w),fldenotestheEuclideanclosureofninCnandoflistheTopologicalboundaryWeassumethatnisinitsstandardrepresentationandthevolumemeasuredVofflisuormalized.Itfollowsfrom[1],[2]thatthekernelfullctionsK(-,.)havethespecialproperties:(l):K(O,w)=K(z,o)=l,z,wEfl;(2):K(z,w)/o1zEfl,wEfl;(3):.13hK(z,z)=oo;(4):K(z,w)-'isasmoothfunctiononC',xC".ofcourse,K(z,w)=K(w,z).Thecomplexcol1jugateoffisdenotedbyf.By5.7of[3]andpolarcoordinates,th…     

有限分形介质中分数阶反应扩散方程及其解析解

建立了有限分形介质中具有吸附效应的分数阶反应扩散积分方程.利用Lap lace变换、广义有限H ankel变换及其相应的逆变换得到了以M ittag-Leffler函数为主要形式的解析解,并研究了解的渐近性态.     

Periodic dyadic wavelets and coding of fractal functions

Recently, using the Walsh-Dirichlet type kernels, the first author has defined periodic dyadic wavelets on the positive semiaxis which are similar to the Chui-Mhaskar trigonometric wavelets. In this paper we generalize this construction and give examples of applications of periodic dyadic wavelets for coding the Riemann, Weierstrass, Schwarz, van der Waerden, Hankel, and Takagi fractal functions.     

相伴于非散度型椭圆算子的Riesz变换的L~p有界性

本文利用小波方法在一般阶的非散度椭圆算子的系数BMO模非常小的情形下,证明了广义 Riesz变换的 L~p(2≤p<+∞)有界性。     

Hankel transforms of generalized Motzkin numbers

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.     

On the Hartley superconvolution

In this paper we introduce some superconvolutions related to the Hartley transform, and apply them to solve an integral equation of Toeplitz plus Hankel type.     

对称反对称多重尺度函数的构造

１　多重小波的定义和双尺度相似变换 作为一种分析工具,小波已经运用在各种领域,并取得了显著的成果．近年来,多重小波成为小波研究的热点．Ｉ．Ｄａｕｂｅｃｈｉｅｓ［１］已经证明,对单重小波,除Ｈａｒｒ基外不存在对称和反对称的有紧支集的小波正交基．而多重小波则不受这一限制． 利用分形插值的方法,Ｇｅｒｏｎｉｍｏ、Ｈａｒｄｉｎ和 Ｍａｓｓｏｐｕｓｔ［２］等构造出了ＧＨＭ多重小波,相应的多重尺度函数和多重小波函数如图１和图２所示．ＧＨＭ多重小波的两个尺度函数都是对称的,相应的小波函数则一个对称另一个反对称;…     

Wavelet transform and radon transform on the quaternion Heisenberg group

Let Q be the quaternion Heisenberg group,and let P be the affine automorphism group of Q.We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on L2(Q).A class of radial wavelets is constructed.The inverse wavelet transform is simplified by using radial wavelets.Then we investigate the Radon transform on Q.A Semyanistyi–Lizorkin space is introduced,on which the Radon transform is a bijection.We deal with the Radon transform on Q both by the Euclidean Fourier transform and the group Fourier transform.These two treatments are essentially equivalent.We also give an inversion formula by using wavelets,which does not require the smoothness of functions if the wavelet is smooth.In addition,we obtain an inversion formula of the Radon transform associated with the sub-Laplacian on Q.