Sobolev圆盘代数的不变子空间

本文研究了Sobolev圆盘代数R(D)上的乘法算子M_z的不变子空间,完全刻画了余维有限的不变子空间的结构．     

Wavelet packets in Sobolev space

Wavelet packets in Sobolev space H^s (?) are constructed and their orthogonal properties are derived. Using convolution transform theory, boundedness results for the wavelet packets are obtained in the B_{p, ?} (?) space. Examples of wavelet packets in Sobolev space are given.     

Invariant Subspaces for Compact-Friendly Operators in Sobolev Spaces

In this note we extend the concept of compact-friendlyness, defined in the literature for operators on a Banach lattice, to the case of operators on Sobolev spaces and derive the existence of invariant subspaces for compact-friendly operators of this type.     

Sobolev圆盘代数的不变子空间

研究了Sobolev圆盘代数R(D)上乘自变量算子M_z的不变子空间,给出了M_z在任何不变子空间上限制的基本性质,证明了M_z分别限制在两个不变子空间上酉等价当且仅当这两个不变子空间相等,并描述了M_z的一类公共零点在边界的不变子空间的结构.     

Dual Wavelet Frames and Riesz Bases in Sobolev Spaces

This paper generalizes the mixed extension principle in L ₂(ℝ ^d ) of (Ron and Shen in J. Fourier Anal. Appl. 3:617–637, 1997) to a pair of dual Sobolev spaces H ^s (ℝ ^d ) and H ^−s (ℝ ^d ). In terms of masks for φ,ψ ¹,…,ψ ^L ∈H ^s (ℝ ^d ) and , simple sufficient conditions are given to ensure that (X ^s (φ;ψ ¹,…,ψ ^L ), forms a pair of dual wavelet frames in (H ^s (ℝ ^d ),H ^−s (ℝ ^d )), where

Subelliptic Sobolev Spaces for Manifolds with Symmetries

Given a group of symmetries on a (generally non-compact) differentiable manifold, we construct invariant locally subelliptic operators, prove Sobolev inequalities and verify existence of correspondent minimizers. The results apply, in particular, to a class of singular elliptic operators on domains in R^N with singularity on the boundary. Mathematics Subject Classifications (2000) 35H20, 35J20, 40A30, 22E30, 43A85.K. Tintarev: Research supported by a grant from Vetenskaprådet.     

Cheeger Type Sobolev Spaces for Metric Space Targets

In this paper, we consider the natural generalization of Cheeger type Sobolev spaces to maps into a metric space. We solve Dirichlet problem for CAT(0)-space targets, and obtain some results about the relation between Cheeger type Sobolev spaces for maps into a Banach space and those for maps into a subset of that Banach space. We also prove the minimality of upper pointwise Lipschitz constant functions for locally Lipschitz maps into an Alexandrov space of curvature bounded above.     

Hardy空间上某些解析Toeplitz算子的换位及约化子空间

讨论了Hardy空间上以非退化有界单叶解析函数的幂为符号的解析Toeplitz算子的换位.并且刻划了符号为三个Blaschke因子积的解析Toeplitz算子的约化子空间.     

实直线周期子集上的向量值子空间弱Gabor双框架

因其在多路复用技术中的潜在应用,超框架(又称向量值框架)和子空间框架受到了众多数学家和工程专家的关注.弱双框架是希尔伯特空间中双框架的推广.本文研究实直线周期子集上的向量值子空间弱Gabor双框架(WGBFs),即L~2(S,C~L)中的WGBFs,其中S是R上的周期子集.利用Zak变换矩阵方法,得到了WGBFs的刻画,它将构造WGBFs的问题归结为设计有限阶Zak变换矩阵;给出了WGBFs的一个例子定理;导出了WGBFs的一个稠密性定理.     

A Modified Weak Galerkin Finite Element Method for Sobolev Equation

For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete $H^1$ and $L^2$ norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.     

Decay of Dissipative Equations and Negative Sobolev Spaces

We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible Navier-Stokes equations and the Boltzmann equation. In particular, the optimal decay rates of the higher-order spatial derivatives of solutions are obtained. The negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis.     

带边界Riemann流形上的Sobolev空间等价范数

对具光滑边界αＭ的Ｒｉｅｍａｎｎ流形（Ｍ，ｇ），本文建立了Ｓｏｂｏｌｅｖ空间Ｈ（Ｍ）的等价范数     

Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces

This paper mainly concerns a tuple of multiplication operators defined on the weighted and unweighted multi-variable Bergman spaces, their joint reducing subspaces and the von Neumann algebra generated by the orthogonal projections onto these subspaces. It is found that the weights play an important role in the structures of lattices of joint reducing subspaces and of associated von Neumann algebras. Also, a class of special weights is taken into account. Under a mild condition it is proved that if those multiplication operators are defined by the same symbols, then the corresponding von Neumann algebras are $*$-isomorphic to the one defined on the unweighted Bergman space.     

Embedding Theorems for a Certain Function Class of Sobolev Type on Metric Spaces

Given a metric space with a Borel measure , we consider a class of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function p-summable with respect to . We prove some analogs of the classical theorems on embedding Sobolev function classes into Lebesgue spaces.     

Closed Complemented Subspaces of Banach Spaces and Existence of Bounded Quasi-linear Generalized Inverses

In this article, an equivalent condition for the existence of a bounded quasi-linear (BQL) generalized inverse of a closed linear operator with respect to projector between two Banach spaces is given. Using the BQL generalized inverse, we give a necessary and su?cient condition for a closed linear subspace in a Banach space to be complemented. Finally, an application of the main results to the Saddle–Node bifurcation theorem from multiple eigenvalues in nonlinear analysis is given.     

On the Spectral Multiplicity of Some Volterra Operators in Sobolev Spaces

Mathematical Notes -     

Convergence of Cascade Algorithms in Sobolev Spaces for Perturbed Refinement Masks

In this paper, the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks.     

On a Class of Weak Nonhomogeneous Affine Bi-frames for Reducing Subspaces of L~2(R~d)

For refinable function-based affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame(WNABF).Under the setting of reducing subspaces of L~2(R~d), we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.     

Central Subspaces of Banach Spaces

In this paper we study Banach spaces that admit weighted Chebyshev centres for finite sets. Such spaces have been extensively studied recently by Veselý using the approach of finitely intersecting balls. Following his approach we exhibit large classes of Banach spaces that have this property. Certain stability results for spaces of vector valued continuous and Bochner integrable functions are also obtained.