The structure of compact disjointness preserving operators on continuous functions

Let T be a compact disjointness preserving linear operator from C₀(X) into C₀(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Σ_n δ ?h_n for a (possibly finite) sequence {x_n }_n of distinct points in X and a norm null sequence {h_n }_n of mutually disjoint functions in C₀(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Calderón approach to an elliptic boundary problem

We consider a boundary problem for an elliptic system in a bounded region Ω ? ?ⁿ and where the spectral parameter is multiplied by a discontinuous weight function ω (x) = diag(ω₁(x), …, ω_N (x)). The problem is considered under limited smoothness assumptions and under an ellipticity with parameter condition. Recently, this problem was studied under the assumption that the ω_j (x)^–1 are essentially bounded in Ω. In this paper we suppose that ω (x) vanishes identically in a proper subregion Ω of Ω and that the ω_j (x)^–1 are essentially bounded in . Then by using methods which are a variant of those used in constructing the Calderón projectors for the boundary Γ of Ω, we shall derive results here which will enable us in a subsequent work to apply the ideas of Calderón to develop the spectral theory associated with the problem under consideration here (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundedness and compactness of an integral operator between <Emphasis Type="Italic">H</Emphasis><Superscript>∞</Superscript> and a mixed norm space on the polydisk

This addendum to [1] completely characterizes the boundedness and compactness of a recently introduced integral type operator from the space of bounded holomorphic functions H ^∞(\(\mathbb{D}^n \)) on the unit polydisk \(\mathbb{D}^n \) to the mixed norm space

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with p, q ∈ [1,∞) and α = (α₁, ..., α _n ) such that α _j > ?1 for every j = 1, ..., n. We show that the operator is bounded if and only if it is compact and if and only if g ∈

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, where \(\vec q\) = (q, ..., q).

     

Products of integral-type operators and composition operators from the mixed norm space to Bloch-type spaces

Siberian Mathematical Journal - We give a complete picture of the boundedness and compactness of the products of integral-type operators and composition operators from the mixed norm space to...     

Integral-type operators acting between weighted-type spaces on the unit ball

Let B denote the unit ball in Cⁿ and H(B) the space of all holomorphic functions on B. We study the boundedness and compactness of the following integral-type operators

     

A variational characterisation of spherical designs

In this paper we first establish a new variational characterisation of spherical designs: it is shown that a set , where , is a spherical L-design if and only if a certain non-negative quantity A_L,N(X_N) vanishes. By combining this result with a known “sampling theorem” for the sphere, we obtain the main result, which is that if is a stationary point set of A_L,N whose “mesh norm” satisfies h_XN<1/(L+1), then X_N is a spherical L-design. The latter result seems to open a pathway to the elusive problem of proving (for fixed d) the existence of a spherical L-design with a number of points N of order (L+1)^d. A numerical example with d=2 and L=19 suggests that computational minimisation of A_L,N can be a valuable tool for the discovery of new spherical designs for moderate and large values of L.     

Some properties of the class of positive Dunford-Pettis operators

We characterize Banach lattices for which each positive Dunford-Pettis operator is M-weakly compact (resp. L-weakly compact) and we give some consequences.     

随机矩阵函数Kronecker积的谱半径的不等式

证明了随机矩阵函数Kronecker积的谱半径的几个不等式.     

加权Begman空间的加权复合算子的本性模

利用上极限,给出了单位球上加权Bergman空间的加权复合算子的本性模的表示．     

MKdV方程的多辛Fourier拟谱方法

基于谱微分矩阵方法,给出MKdV方程的多辛Fourier拟谱格式及其相应多辛离散守恒律,证明了它等价于通常的Fourier拟谱格式．数值结果表明,格式对于长时间计算具有稳定性与高精度．