Dyadic Bivariate Wavelet Multipliers in L^2（R@2）

The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation (where A is any expansive matrix with integer entries and |detA| = 2) wavelet multipliers in twodimensional case were completely characterized by Wutam Consortium (1998) and Li Z., et al. (2010). But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix with the absolute value of determinant not 2 in L ²(ℝ²). In this paper, we choose $2I_2 = \left( {{*{20}c} 2 & 0 \\ 0 & 2 \\ } \right)$2I_2 = \left( {\begin{array}{*{20}c} 2 & 0 \\ 0 & 2 \\ \end{array} } \right) as the dilation matrix and consider the 2I ₂-dilation multivariate wavelet Φ = {ψ ₁, ψ ₂, ψ ₃}(which is called a dyadic bivariate wavelet) multipliers. Here we call a measurable function family f = {f ₁, f ₂, f ₃} a dyadic bivariate wavelet multiplier if Y₁ = { F ^{- 1} ( f₁ [^(y₁ )] ),F ^{- 1} ( f₂ [^(y₂ )] ),F ^{- 1} ( f₃ [^(y₃ )] ) }\Psi _1 = \left\{ {\mathcal{F}^{ - 1} \left( {f_1 \widehat{\psi _1 }} \right),\mathcal{F}^{ - 1} \left( {f_2 \widehat{\psi _2 }} \right),\mathcal{F}^{ - 1} \left( {f_3 \widehat{\psi _3 }} \right)} \right\} is a dyadic bivariate wavelet for any dyadic bivariate wavelet Φ = {ψ ₁, ψ ₂, ψ ₃}, where [^(f)]\hat f and F ⁻¹ denote the Fourier transform and the inverse transform of function f respectively. We study dyadic bivariate wavelet multipliers, and give some conditions for dyadic bivariate wavelet multipliers. We also give concrete forms of linear phases of dyadic MRA bivariate wavelets.     

An Effective Line Search for the Subgradient Method

One of the main drawbacks of the subgradient method is the tuning process to determine the sequence of steplengths. In this paper, the radar subgradient method, a heuristic method designed to compute a tuning-free subgradient steplength, is geometrically motivated and algebraically deduced. The unit commitment problem, which arises in the electrical engineering field, is used to compare the performance of the subgradient method with the new radar subgradient method.Communicated by M. SimaanThis research was supported by the Spanish Government, CICYT Grant TAP99-1075-C02-01. We acknowledge the technical support from Logilab (HEC, University of Geneva) and especially the valuable remarks and suggestions of the referees.     

算子值傅里叶乘子与向量值边值问题最大正则性

向量值L^p空间上的算子值傅里叶乘子由于L．Weis在2000年的重要工作而成为泛函分析的热点之一，其对R-有界性创造性的应用使这个领域的研究耳目一新，新的结果层出不穷．本文的目的是介绍算子值傅里叶乘子的这些最新进展，以及它们在向量值边值问题最大正则性方面的应用．包括N．J．Kalton和G．Lancien给出的关于L^p-最大正则性的反例．Besov空间和Triebel空间上的算子值傅里叶乘子以及在Besov空问和Triebel空间意义下的最大正则性也是我们要介绍的内容．     

Optimization approach to the design of frequency sampling filters

Many digital signal processing applications require linear phase filtering. For applications that require narrow-band linear phase filtering, frequency sampling filters can implement linear phase filters more efficiently than the commonly used direct convolution filter. In this paper, a technique is developed for designing linear phase frequency sampling filters. A frequency sampling filter approximates a desired frequency response by interpolating a frequency response through a set of frequency samples taken from the desired frequency response. Although the frequency response of a frequency sampling filter passes through the frequency samples, the frequency response may not be well behaved between the specific samples. Linear programming is commonly used to control the interpolation errors between frequency samples. The design method developed in this paper controls the interpolation errors between frequency samples by minimizing the mean square error between the desired and actual frequency responses in the stopband and passband. This design method describes the frequency sampling filter design problem as a constrained optimization problem which is solved using the Lagrange multiplier optimization method. This results in a set of linear equations which when solved determine the filter's coefficients.This work was partially funded by The National Supercomputing Center for Energy and the Environment, University of Nevada Las Vegas, Las Vegas, Nevada and by NSF Grant MIP-9200581.     

规范场静态解的稳定性

对有规范条件或约束的非线性理论,研究了其驻点的Hessian形式.指出了规范场的经典解的稳定性由包含拉格朗日乘子贡献的有效拉氏量的二阶变分决定.     

Cn中多圆柱上广义Bloch空间的点乘子

讨论了Cn(n>1)中多圆柱上广义Bloch空间βp上的点乘子,根据p、q的不同情况得到βp空间到βq空间所有的点乘子,得到(1)当p<1时M(βp)=βp;(2)当p≥1时M(βp)=c;(3)当p>q时M(βp,βq)={0};(4)当p<q<1时M(βp,βq)=βq;(5)当p<1≤q时M(βp,βq)=Jp,q∩βq;(6)当1≤p<q时M(βp,βq)=c.     

A note on operator‐valued Fourier multipliers on Besov spaces

Let X be a Banach space. We show that each m : ? \ {0} → L (X ) satisfying the Mikhlin condition sup_{x ≠0}(‖m (x )‖ + ‖xm ′(x )‖) < ∞ defines a Fourier multiplier on B ^s _p,q (?; X ) if and only if 1 < p < ∞ and X is isomorphic to a Hilbert space; each bounded measurable function m : ? → L (X ) having a uniformly bounded variation on dyadic intervals defines a Fourier multiplier on B ^s _p,q (?; X ) if and only if 1 < p < ∞ and X is a UMD space. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类无穷矩阵代数的乘法序列连续性

设λ，μ是两个序列空间并有符号弱滑脊性，（λ，μ）是变换λ进入μ的无穷矩阵算子所成的无穷矩阵代数，本文研究了这类代数的强，Mackey、弱乘法序列连续性问题。     

Spherical convolution operators in spaces of variable Hölder order

In this paper, we study the images of operators of the type of spherical potential of complex order and of spherical convolutions with kernels depending on the inner product and having a spherical harmonic multiplier with a given asymptotics at infinity. Using theorems on the action of these operators in Hölder-variable spaces, we construct isomorphisms of these spaces. In Hölder spaces of variable order, we study the action of spherical potentials with singularities at the poles of the sphere. Using stereographic projection, we obtain similar isomorphisms of Hö lder-variable spaces with respect to n-dimensional Euclidean space (in the case of its one-point compactification) with some power weights.     

COEFFICIENT MULTIPLIERS ON MIXED NORM SPACES

§1　IntroductionSuppose thatf is analytic in the open unit disc D in the complex plane.We defineMp(r,f) =12π∫2π0 | f(reiθ) | pdθ1 / p,0

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