A Quadrature Formula Based On Sampling In Meyer Wavelet Subspaces

In this paper we discuss a weighted trapezoidal rule based on sampling in Meyer wavelet subspaces. For a wide class of functions, we obtain convergence and error bounds. Some examples are given to construct sampling functions.     

Irregular Sampling in Wavelet Subspaces

As a particular wavelet subspace, the Paley-Wiener space has both regular and irregular sampling theorems. A regular sampling theorem in general wavelet subspaces has been established for several years. In this paper, we discuss the irregular sampling problem in wavelet subspaces.     

Positive Sampling in Wavelet Subspaces

This paper is devoted to the discussion of a “hybrid” sampling series, a series of translates of a nonnegative summability function used in place of an orthogonal scaling function. The coefficients in the series are taken to be sampled values of the function to be approximated. This enables one to avoid the integration which arises in the other series. The approximations based on this hybrid series have certain desirable convergence properties: they are locally uniformly convergent for locally continuous functions, they have quadratic uniform convergence rate for functions in certain Sobolev spaces, they are locally bounded when the function is locally bounded and therefore, in particular, Gibbs' phenomenon is avoided. Numerical experiments are given to illustrate the theoretical results and to compare these approximations with the scaling function approximations.     

Truncation Error on Wavelet Sampling Expansions

We estimate the truncation error of sampling expansions on translationinvariant spaces, generated by integer translations of a single functionand on wavelet subspaces of L ₂(R). As a byproduct of themain result, we get the classical Jagerman's bound for Shannon's samplingexpansions. We also examine this error on certain wavelet sampling expansions.     

有限区间小波子空间上的采样定理及H~2(I)空间中函数的逼近表示

给出有限区间 [0 ,L ]小波子空间上的 Shannon型采样定理 .它是应用再生核空间理论和Riesz基的对偶性质得到的 .另外 ,根据得到的采样定理 ,讨论了 Sobolev空间 H20 ( I)和 H2 ( I)中的函数、一阶导函数及二阶导函数的逼近表示 .最后给出相应的数值算例     

Local Sampling and Reconstruction in Shift-Invariant Spaces and Their Applications in Spline Subspaces

The local reconstruction from samples is one of the most desirable properties for many applications in signal processing. Local sampling is practically useful since we need only to consider a signal on a bounded interval and computer can only process finite samples. However, the local sampling and reconstruction problem has not been given as much attention. Most of known results concern global sampling and reconstruction. There are only a few results about local sampling and reconstruction in spline subspaces. In this article, we study local sampling and reconstruction in general shift-invariant spaces and multiple generated shift-invariant spaces with compactly supported generators. Then we give several applications in spline subspaces and multiple generated spline subspaces.     

小波空间的非均匀采样及其重构

信号的采样问题，就是探讨采样集满足什么条件时，能够重建信号，如何重建信号．对于f(x)∈L^2(R)，这里证明了，当采样集满足一定的条件时，适当选择小波基，可以重建信号，并且考虑了用迭代重构算法来重建信号，得到了具体的逼近精度．     

Analysis on an ODE arisen from studying the shape of a red blood cell

We study the existence problem of a special solution to the Helfrich functional such that it corresponds to a surface of the shape of a red blood cell. The Helfrich functional is also a perturbation of the Willmore functional involving some parameters with physical meanings. With the expected symmetry of the surface, it reduces to an analysis on an ODE with certain shape requirements. We discover a sufficient condition on the parameters which ensures the existence of such a special solution to the ODE.     

Pointwise Convergence and Uniform Convergence of Wavelet Frame Series

Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.     

考虑检验错误的集团抽样检验接收概率函数

本文给出存在集团检验误差时的集团抽样检验接受概率计算公式,该公式可用于设计抽样方案、分析集团检验错误对抽样方案的影响.采用计算机模拟抽样检验的方法对给出的公式加以验证,证明了该所给公式的正确性.同时通过对集团检验错误存在与否的抽样检验特征(OC)曲线的比较,指出:以往的集团抽样检验方案设计,都是在假设无检验误差前提下设计的,在抽样检验中,若存在检验错误,会严重影响抽样检验的接收概率,使抽样检验结果不能客观地反映检验批的质量.     

Hermite型多元样本定理及Sobolev类上混淆误差的估计

本文证明了Hermite型多元样本定理,并由此确定了Sobolev类上混淆误差阶的精确估计．     

Hermite型多元样本定理及Sobolev类上混淆误差的估计

本文证明了Hermite型多元样本定理,并由此确定了Sobolev类上混淆误差阶的精确估计.     

Bayesian Methods for Wavelet Series in Single-Index Models

Single-index models have found applications in econometrics and biometrics, where multidimensional regression models are often encountered. This article proposes a nonparametric estimation approach that combines wavelet methods for nonequispaced designs with Bayesian models. We consider a wavelet series expansion of the unknown regression function and set prior distributions for the wavelet coefficients and the other model parameters. To ensure model identifiability, the direction parameter is represented via its polar coordinates. We employ ad hoc hierarchical mixture priors that perform shrinkage on wavelet coefficients and use Markov chain Monte Carlo methods for a posteriori inference. We investigate an independence-type Metropolis-Hastings algorithm to produce samples for the direction parameter. Our method leads to simultaneous estimates of the link function and of the index parameters. We present results on both simulated and real data, where we look at comparisons with other methods.     

小波级数的Bouligand维数(英)

本文讨论小波级数的上、下Buoligangd维数，在小波级数满足一定的条件下，给出了与Weierstrass函数相应的结果．     

Error estimates for irregular sampling of band-limited functions on a locally compact Abelian group

Band-limited functions f can be recovered from their sampling values (f(x_i)) by means of iterative methods, if only the sampling density is high enough. We present an error analysis for these methods, treating the typical forms of errors, i.e., jitter error, truncation error, aliasing error, quantization error, and their combinations. The derived apply uniformly to whole families of spaces, e.g., to weighted L^p-spaces over some locally compact Abelian group with growth rate up to some given order. In contrast to earlier papers we do not make use of any (relative) separation condition on the sampling sets. Furthermore we discard the assumption on polynomial growth of the weights that has been used over Euclidean spaces. Consequently, even for the case of regular sampling, i.e., sampling along lattices in G, the results are new in the given generality.     

套代数子空间的端点

设d为套代数AlgN的子空间且包含AlgN的所有一秩算子．利用预零化子d⊥中一秩算子,我们给出了单位球d1中端点的刻画．     

关于压缩算子的不变子空间

证明关于压缩算子的如下不变子空间定理：如果T是Hilbert空间H上的压缩算子,且集合Z’={λ∈D;存在z∈H,使得‖z‖=1,且‖（λ-T）z‖＜1/3(1-‖λ‖}是开单位圆D的控制集,那么T有非平凡的不变子空间,这个定理包含了S.Brown,B.Chevreau,C.fPearcy和B.Beauzamy的两个重要结果作为特殊情况,特别是,为个定理包含了S.Brown等人的Hilbert空间上的每个具有厚谱的压缩算子都有平凡的不变子空间这个重要结果作为特殊情况。     

复平面上解析Banach空间的拟不变子空间

讨论复平面上解析Banach空间具有任意指标的拟不变子空间的存在性问题.首先给出一类复平面上解析Banach空间存在任意指标拟不变子空间的判定定理.作为应用,证明了Fock型空间F~p(C)={f∈Hol(C):1/π∫_C|f(z)|~pe~(-|z|~2)dA(z)+∞,1≤p+∞}与Hilbert空间H={f∈Hol(C):1/π∫_C|f(z)|~2e~(-|z|)dA(z)+∞}具有任意指标的拟不变子空间.     

关于L2(Rd)中仿射子空间小波标架的一个注记

研究了L2(Rd)的有限生成仿射子空间中小波标架的构造.证明了任意有限生成仿射子空间都容许一个具有有限多个生成元的Parseval小波标架,并且得到了仿射子空间是约化子空间的一个充分条件.对其傅里叶变换是一个特征函数的单个函数生成的仿射子空间,得到了与小波标架构造相关的投影算子在傅里叶域上的明确表达式,同时也给出了一些例子.