E小波乘子的某些应用

Let E=(1 1 1 -1) or (0 1 2 0). A measurable function v is called an E-waveletmultiplier if (rψ)v is an E-wavelet whenever ψ is an E-wavelet. Some characterizations and applications of E-wavelet multiplier were considered in [1]. In this paper, we give some other applications of E-wavelet multiplier, and prove that the set of all MRA E-wavelets is arcwise connected.     

一类带限的插值小波

Ｓｈａｎｎｏｎ尺度函数具有带限性质，正交性质、取样性质，但它不在Ｌ（Ｒ）中，本文引入小波，它的尺度函数不仅具有上述性质而且在Ｌ（Ｒ）中，甚至更多。     

多频率多函数小波

本文把通过方向多分辨分析构造的由一个函数生成的多频率小波推广到由有限个函数生成的多频率小波，给出由n2j1 j2个函数φ1,…φn,ψ1,…ψn(2j1 j2-1)的平移生成Vj(l)空间的Riesz基的充分必要条件．     

紧支撑的最小能量框架

基于仿酉矩阵扩充方法,本文构造了一维d带紧支撑的最小能量框架,给出了一维d带紧支撑最小能量框架的显式构造算法.所构造的最小能量框架的支撑不超过尺度函数的支撑.当所给的尺度函数具有对称性时,研究了紧支撑对称最小能量框架的结构.最后,构造了两个算例.     

Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green-Naghdi equations

This paper presents a multiresolution discontinuous Galerkin (DG) scheme for the adaptive solution of Boussinesq-type equations. The model combines multiwavelet (MW)–based grid adaptation with a DG solver based on the system of fully nonlinear and weakly dispersive Green-Naghdi (GN) equations. The key feature of the adaptation procedure is to conduct a multiresolution analysis using MWs on a hierarchy of nested grids to improve the efficiency of the reference DG scheme on a uniform grid by computing on a locally refined adapted grid. This way, the local resolution level will be determined by manipulating MW coefficients controlled by a single user-defined threshold value. The proposed adaptive multiwavelet DG solver for GN equations is assessed using several benchmark problems related to wave propagation and transformation in nearshore areas. The numerical results demonstrate that the proposed scheme retains the accuracy of the reference scheme, while significantly reducing the computational cost.     

Frame multiresolution analysis and infinite trees in Banach spaces on locally compact abelian groups

We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaceson locally compact abelian groups including modulation spaces.     

求解双曲型守恒律方程的一类自适应多分辨方法

针对双曲型守恒律方程问题,发展一种有效的自适应多分辨分析方法.通过对嵌套网格上的数值解构造离散多分辨分析,建立小波系数与多层嵌套网格点之间的对应关系.对于小波系数较大的网格点采用高精度WENO格式计算,其余区域则直接采用多项式插值.数值试验表明,该方法在保持原规则网格方法的精度和分辨率的同时,显著地减少计算的CPU时间.     

Frames of p-adic wavelets and orbits of the affine group

The general construction of frames of p-adic wavelets is described. We consider the orbit of a generic mean zero locally constant function with compact support (mean zero test function) with respect to the action of the p-adic affine group and show that this orbit is a uniform tight frame. We discuss the relations of this result with the multiresolution wavelet analysis. The text was submitted by the authors in English.     

Multidimensional basis of p-adic wavelets and representation theory

A multidimensional basis of p-adic wavelets is constructed. The relation of the constructed basis to a system of coherent states i.e., orbit of action) for some p-adic group of linear transformations is discussed. We show that the set of products of the vectors from the constructed basis and p-roots of unity is the orbit of the corresponding p-adic group of linear transformations. The text was submitted by the authors in English.