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1.
小波标架的稳定性   总被引:3,自引:0,他引:3  
在小波分析理论中,标架起着十分重要的作用.对(∈L~2(R)和a>1.b>0,I.Daubechies给出了{a~(j/2)((a~jx—kb):j,k ∈Z}构成L~2(R)的标架的充分条件.近年来,人们对小波标架的稳定性进行了大量研究.首先把Kadec定理推广到高维情形,然后研究当(,{a~j},{k}同时变化时标架的稳定性.特别地,我们给出{a~j}扰动时标架的稳定性.  相似文献   

2.
罗宗俊 《数学杂志》1996,16(2):163-170
本文讨论了数学模型:max{f(x)│f(x)=min(1≤j≤n)〔c1jx1j+c2jx2j〕,x∈D},其中D={x│x={xij},nΣ(j=1)xij=a,i=1,2,xij≥0且为整数},并给出了一个拟多项式算法。  相似文献   

3.
本文建立多线性算子TA1,A2,…Akf(x)=p.v∫RneiP(x,y)Ω(x-y)|x-y|n+M-kkj=1Rmj(Aj;x,y)f(y)dy,n2,的一个变形的sharp估计,其中P(x,y)是Rn×Rn上的实值多项式,Ω是零阶齐性函数且满足某种消失性条件,M=∑kj=1mj,Rmj(Aj;x,y)表示Aj在x点关于y的mj阶Taylor级数余项,对所有满足|α|=mj-1(j=1,2,…,k)的指标α,DαAj∈BMO(Rn).作为sharp估计的推论,得到了算子TA1,A2…Ak在Lp(1<p<∞)上的有界性.  相似文献   

4.
本文讨论了如下一类线性errors-in-variables模型——多元线性结构关系模型β′xk+α=0,ξk=xk+εk.{k=1,2,…,n.其中,{xk:k=1,2,…,n}为一组i.i.d.的m维随机向量,{εk:k=1,2,…,n}是i.i.d.的随机误差,E(ε1)=0,Var(ε1)=σ2Im.且{xk:k=1,2,…,n}与{εk:k=1,2,…,n}相互独立.在一些条件下,我们证明了估计量β,α,σ2的强相合性、唯一性,并给出了估计量的收敛速度为o(n-1-1q),这里q∈[1,2).对于E(x1)u1和Var(x1)Vx的估计也得出了同样的结果  相似文献   

5.
本文研究n阶时滞差分方程的边值问题:x(k+n)=f(k,xk(),x(k),x(k+1),…,x(k+n-1)),k∈IT,x(m)=φ(m),m∈I-r,x(1)=a1,x(2)=a2,…,x(n-2)=an-2,x(T)=A,{得到了解的存在性和唯一性的结果.  相似文献   

6.
高维空间中半线性波动方程的Sobolev指数   总被引:6,自引:0,他引:6  
GustavoPonce与ThomasC.Sideris[4]猜测对一些具有特殊非线性项的半线性波动方程,如ut-△u=uk(Du)α(x∈Rn,k∈Z+,l=|α|2),其中Sobolev指数会在n2与(n2+1)之间.文[4]中,在x∈R3时,回答了这一问题.本文在n3维空间中,得到了半线性波动方程ut-△u=uk(Du)α(x∈Rn,k∈Z+,l=|α|2)的Sobolev指数为max{n2+12,(n2-1)·l-3l-1+2},此数确实在区间[n2+12,n2+1]中.  相似文献   

7.
用算术函数a(n)表示n阶非同构Abel群的个数,令Ak(x)=∑/n≤x/a(n)=k 1,Ak(x;h)=Ak(x+j)-Ak(x)。  相似文献   

8.
黄达人  王伟 《数学进展》1997,26(2):165-180
本文考虑一般细分方程ψi(x)=Σ1≤j≤NΣk∈Zcij(k)ψj(2x-k),解的存在性,正则性和稳定性,及{ψi}1≤i≤N产生L^p多分辨率分析的条件。  相似文献   

9.
§1.Forthesystemx=-y+δx+lx2+ny2=P(x,y),y=x(1+ax-y)=Q(x,y),{(1.1)wecanfindin[1]thefolowing:ConjectureI.Assume1a<0,n>1,n+l>0,na2...  相似文献   

10.
设{αk}∞k=-∞为正数缺项序列,满足infkαk+1/dk=α>1,Ω(y′)为Besov空间B0,11(Sn-1)上的函数,其中Sn-1为Rn(n2)上的单位球面.本文证明:若∫Sn-1Ω(y′)dσ(y′)=0,则离散型奇异积分TΩ(f)(x)=∑∞k=-∞∫Sn-1f(x-αky′)Ω(y′)dσ(y′)和相关的极大算子TΩ(f)(x)=supN∑∞k=N∫Sn-1f(x-αky′)Ω(y′)dσ(y′)均在L2(Rn)上有界.上述结果推广了Duoandikoetxea和RubiodeFrancia[1]在L2情形下的一个结果  相似文献   

11.
In this paper, we present the conditions on dilation parameter {sj}j that ensure a discrete irregular wavelet system to be a frame on L2(Rn), and for the wavelet frame we consider the perturbations of translation parameter b and frame function ψ respectively.  相似文献   

12.
In this paper we deal with multidimensional wavelets arising from a multiresolution analysis with an arbitrary dilation matrix A, namely we have scaling equations $$\varphi ^s (x) = \sum\limits_{k \in \mathbb{Z}^n } {h_k^s \sqrt {|\det A|} \varphi ^1 } (Ax - k) for s = 1, \ldots ,q,$$ where ?1 is a scaling function for this multiresolution and ?2, …, ?q (q=|det A |) are wavelets. Orthogonality conditions for ?1, …, ?q naturally impose constraints on the scaling coefficients $\{ h_k^s \} _{k \in \mathbb{Z}^n }^{s = 1, \ldots ,q} $ , which are then called the wavelet matrix. We show how to reconstruct functions satisfying the scaling equations above and show that ?2, …, ?q always constitute a tight frame with constant 1. Furthermore, we generalize the sufficient and necessary conditions of orthogonality given by Lawton and Cohen to the case of several dimensions and arbitrary dilation matrix A.  相似文献   

13.
本篇文章给出一类$L^{2}(\mathbb{R}^{n})$, $n\geq2$的紧支撑不可分正交小波基的具体构造算法,其中正交小波的伸缩矩阵为$\alpha I_{n}~(\alpha\geq2,\ \alpha \in \mathbb{Z})$, $I_{n}$是$n$阶单位矩阵.最后给出两个不可分正交小波基的构造算例.  相似文献   

14.
设S={x1,x2,...,xn}是由n个不同的正整数组成的集合,并设a为正整数.如果一个n阶矩阵的第i行j列元素是S中元素xi和xj的最大公因子的a次幂(xi,xj)a,则称该矩阵为定义在S上的a次幂最大公因子(GCD)矩阵,用(Sa)表示;类似定义a次幂LCM矩阵[Sa].如果存在{1,2,...,n}上的一个置换σ使得xσ(1)|xσ(2)|···|xσ(n),则称S为一个因子链.如果存在正整数k,使得S=S1∪S2∪···∪Sk,其中每一个Si(1ik)均为一个因子链,并且对所有的1i=jk,Si中的每个元素与Sj中的每个元素互素,则称S由有限个互素因子链构成.本文中,设S由有限个互素的因子链构成,并且1∈S.我们首先给出幂GCD矩阵与幂LCM矩阵的行列式的公式,然后证明:如果a|b,则det(Sa)|det(Sb),det[Sa]|det[Sb],det(Sa)|det[Sb].最后我们指出:如果构成S的有限个因子链不互素,则此结论一般不成立.  相似文献   

15.
本文给出伸缩矩阵行列式为2的一类二元半正交小波包的构造算法.该小波包是以频域给出的,随着用于小波包分裂的滤波器选取的不同会得到L2(R2)中形态各异的Riesz基,这样使得L2(R2)中小波基的选择更灵活.  相似文献   

16.
We study the constrained systemof linear equations Ax=b,x∈R(Ak)for A∈Cn×nand b∈Cn,k=Ind(A).When the system is consistent,it is well known that it has a unique ADb.If the system is inconsistent,then we seek for the least squares solution of the problem and consider minx∈R(Ak)||b?Ax||2,where||·||2 is the 2-norm.For the inconsistent system with a matrix A of index one,it was proved recently that the solution is Ab using the core inverse Aof A.For matrices of an arbitrary index and an arbitrary b,we show that the solution of the constrained system can be expressed as Ab where Ais the core-EP inverse of A.We establish two Cramer’s rules for the inconsistent constrained least squares solution and develop several explicit expressions for the core-EP inverse of matrices of an arbitrary index.Using these expressions,two Cramer’s rules and one Gaussian elimination method for computing the core-EP inverse of matrices of an arbitrary index are proposed in this paper.We also consider the W-weighted core-EP inverse of a rectangular matrix and apply the weighted core-EP inverse to a more general constrained system of linear equations.  相似文献   

17.
In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 (R n ) with matrix dilations of the form (Df)(x) =√ 2f(Ax),where A is an arbitrary expanding n × n matrix with integer coefficients,such that |det A| = 2.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.  相似文献   

18.
An orthonormal wavelet system in ℝd, d ∈ ℕ, is a countable collection of functions {ψ j,k }, j ∈ ℤ, k ∈ ℤd, ℓ = 1,..., L, of the form that is an orthonormal basis for L2 (ℝd), where a ∈ GLd (ℝ) is an expanding matrix. The first such system to be discovered (almost 100 years ago) is the Haar system for which L = d = 1, ψ1(x) = ψ(x) = κ[0,1/2)(x) − κ[l/2,1) (x), a = 2. It is a natural problem to extend these systems to higher dimensions. A simple solution is found by taking appropriate products Φ(x1, x2, ..., xd) = φ1 (x12(x2) ... φd(xd) of functions of one variable. The obtained wavelet system is not always convenient for applications. It is desirable to find “nonseparable” examples. One encounters certain difficulties, however, when one tries to construct such MRA wavelet systems. For example, if a = ( 1-1 1 1 ) is the quincunx dilation matrix, it is well-known (see, e.g., [5]) that one can construct nonseparable Haar-type scaling functions which are characteristic functions of rather complicated fractal-like compact sets. In this work we shall construct considerably simpler Haar-type wavelets if we use the ideas arising from “composite dilation” wavelets. These were developed in [7] and involve dilations by matrices that are products of the form ajb, j ∈ ℤ, where a ∈ GLd(ℝ) has some “expanding” property and b belongs to a group of matrices in GLd(ℝ) having |det b| = 1.  相似文献   

19.
In this paper, we consider the limit cycles of a class of polynomial differential systems of the form $\dot{x}=-y, \hspace{0.2cm} \dot{y}=x-f(x)-g(x)y-h(x)y^{2}-l(x)y^{3},$ where $f(x)=\epsilon f_{1}(x)+\epsilon^{2}f_{2}(x),$ $g(x)=\epsilon g_{1}(x)+\epsilon^{2}g_{2}(x),$ $h(x)=\epsilon h_{1}(x)+\epsilon^{2}h_{2}(x)$ and $l(x)=\epsilon l_{1}(x)+\epsilon^{2}l_{2}(x)$ where $f_{k}(x),$ $g_{k}(x),$ $h_{k}(x)$ and $l_{k}(x)$ have degree $n_{1},$ $n_{2},$ $n_{3}$ and $n_{4},$ respectively for each $k=1,2,$ and $\varepsilon$ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot{x}=-y,$ $\dot{y}=x$ using the averaging theory of first and second order.  相似文献   

20.
We consider the problem of characterizing the wavefront set of a tempered distribution \(u\in \mathcal {S}'(\mathbb {R}^{d})\) in terms of its continuous wavelet transform, where the latter is defined with respect to a suitably chosen dilation group \(H\subset \mathrm{GL}(\mathbb {R}^{d})\). In this paper we develop a comprehensive and unified approach that allows to establish characterizations of the wavefront set in terms of rapid coefficient decay, for a large variety of dilation groups. For this purpose, we introduce two technical conditions on the dual action of the group H, called microlocal admissibility and (weak) cone approximation property. Essentially, microlocal admissibility sets up a systematic relationship between the scales in a wavelet dilated by \(h\in H\) on one side, and the matrix norm of h on the other side. The (weak) cone approximation property describes the ability of the wavelet system to adapt its frequency-side localization to arbitrary frequency cones. Together, microlocal admissibility and the weak cone approximation property allow the characterization of points in the wavefront set using multiple wavelets. Replacing the weak cone approximation by its stronger counterpart gives rise to single wavelet characterizations. We illustrate the scope of our results by discussing—in any dimension \(d\ge 2\)—the similitude, diagonal and shearlet dilation groups, for which we verify the pertinent conditions. As a result, similitude and diagonal groups can be employed for multiple wavelet characterizations, whereas for the shearlet groups a single wavelet suffices. In particular, the shearlet characterization (previously only established for \(d=2\)) holds in arbitrary dimensions.  相似文献   

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