由一元连续小波变换得到的二元连续小波变换及重构公式

讨论了L2(R2)空间中连续小波变换,分别得到由一元变换函数构造二元变换函数的二元小波变换及重构公式,得到重构公式在L2(R2)中范数收敛意义下成立的条件.     

一维连续小波变换

1引言小波分析是近年来迅速发展起来的一门新兴学科,小波分析最显著的特征是频域和时域具有良好局部化特性,可以观察函数的任意细节,被誉为数学的显微镜．它不仅理论深刻,且理论与应用的发展交织在一起,它成功地应用于信噪分离、图像编码、图像的边缘检测、数据压缩、计算机视觉中的多分辨率分析等领域．     

小波包变换及代价函数设计综述

小波包是小波理论的重要组成部分,在非平稳信号特征检测和故障诊断中具有广泛的应用。小波包教学是小波分析教学的一个难点,也是一个较容易忽视的知识点。本文分析了小波包理论,归纳总结了小波包目标函数,以及它们适用的领域,并提出了新的目标函数。本文可以对小波包的教学提供一些新的思路。     

连续小波变换及小波框架算子的一些性质

以泛函分析的观点来考察连续小波变换及小波框架算子，得到了它们的一些性质，并给出了严格证明，弥补了有关献中的不足。     

离散积分小波变换的快速算法

本文讨论了积分小波变换的快速算法,通过尺度函数与小波间的二尺度关系,导出了一个实现积分小波变换的快速计算方法及相应滤波器的构造方法。     

抽象空间常微分方程弱解的存在和唯一性

本研究了抽象空间中初值可题x^1=f(t,x),x(to)=xo的弱解存在和唯一性,并推广了[1]、[2]中的有关结果．     

Journe小波变换像空间描述

1引言1950年N.Aronszjan发表的一篇综述性文章《Theory of reproducing kernels》标志再生核理论的初步形成.由于再生核有许多良好的计算性质,S.Saitoh总结并深入研究再生核基本理论,进一步拓展了再生核的应用领域;徐利治把再生核应用于L~2(B)(B是复平面上的一个区域)中解析函数重积分降维问题,并提出了一个能对一些预先给出的     

抽象与具体函数积分不等式的证明

在区间I上连续、单调的抽象函数的积分不等式证明的基本思路是适当进行积分变换、分拆积分区间，使不等式恒等变形等手段，使能应用函数的单调性质。具体函数的积分不等式的一般证明方法是把被积函数适当缩放、求出最值(或上下确界)等。     

几类一阶微分方程的统一方程和统一变换

在高等数学的微分方程一章中,一阶变量可分离方程是最基本的方程,分离变量后积分,即得通解（通积分）：式中x（s）羊0（否则y一C）,C为积分常数（下同）．对于一阶非齐次线性方程由于其对应的齐次方程将常数U变易为函数U什）,即作变量代换方程（3）就变为关于函数X（X）和变量X的变量可分离方程积分后代入（5）式,即得非齐次线性方程（3）的通解对,右端为零次齐次。数。（于卜齐次方程当机y缸）学VX（否则,变量可分离）,作变换可得变量可分离方程UU‘＋U一J（U）,于是（7）的通解对于伯努利（Bernoulli）方程（n羊0,豆,否…     

Evaluation of a continuous wavelet transform by solving the Cauchy problem for a system of partial differential equations

It is shown that the problem of evaluating the continuous Morlet wavelet transform can be stated as the Cauchy problem for a system of two partial differential equations. The initial conditions for the desired functions, i.e., for the real and imaginary parts of the wavelet transform, are the analyzed function and a vanishing function, respectively. Numerical examples are given.     

Cauchy wavelet transform of ultra-distributions in tube domains

In this paper, Cauchy wavelet transform of ultra-distributions in tube domains is defined and its various properties are studied using the theory of Cauchy integrals and Poisson integrals of ultra-distributions.     

Application of fuzzy differential transform method for solving fuzzy Volterra integral equations

This paper deals with the solutions of fuzzy Volterra integral equations with separable kernel by using fuzzy differential transform method (FDTM). If the equation considered has a solution in terms of the series expansion of known functions, this powerful method catches the exact solution. To this end, we have obtained several new results to solve mentioned problem when FDTM has been applied. In order to show this capability and robustness, some fuzzy Volterra integral equations are solved in detail as numerical examples.     

Numerical inversion of laplace transform via wavelet in partial differential equations

This article presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that P is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulae of listing table (Chen et al., Journal of The Franklin Institute 303 (1977), 267–284) to a minimum expression and obtain the optimal operation speed. The local property of Haar wavelet is fully applied to shorten the calculation process in the task. The operational method presented in this article owns the advantages of simpler computation as well as broad application. We still can obtain satisfying solution even under large matrix. Moreover, we do not have numerically unstable problems. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 536–549, 2014     

Spherical wavelet transform and its discretization

A continuous version of spherical multiresolution is described, starting from continuous wavelet transform on the sphere. Scale discretization enables us to construct spherical counterparts to wavelet packets and scale discrete wavelets. The essential tool is the theory of singular integrals on the sphere. It is shown that singular integral operators forming a semigroup of contraction operators of class (C ₀) (like Abel-Poisson or Gauß-Weierstraß operators) lead in a canonical way to (pyramidal) algorithms.Supported by the Graduiertenkolleg Technomathematik, Kaiserslautern.     

Uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform

ABSTRACT

In this paper, we present some new elements of harmonic analysis related to the right-sided multivariate continuous quaternion wavelet transform. The main objective of this article is to introduce the concept of the right-sided multivariate continuous quaternion wavelet transform and investigate its different properties using the machinery of multivariate quaternion Fourier transform. Last, we have proven a number of uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform.     

Inverse radon transform with one-dimensional wavelet transform

1. IntroductionSince Radon obtained the inverse formula of Radon transform in 1917, different inversemethods such as Fourier inversion, convolution back-projection inversion etc. have beeninvestigated['l']. Wavelet as a useful tool is interested in the inversion of Radon transformin recent years['--']. The application of wavelet analysis to Radon transform was proposedin I4] and [5]. An inversion formula based on continuous wavelet transform was derivedin [6] and [7]. This formula was based…     

Mexican hat wavelet transform of distributions

Theory of Weierstrass transform is exploited to derive many interesting new properties of the Mexican hat wavelet transform. A real inversion formula in the differential operator form for the Mexican hat wavelet transform is established. Mexican hat wavelet transform of distributions is defined and its properties are studied. An approximation property of the distributional wavelet transform is investigated which is supported by a nice example.