Polar Foliations of Symmetric Spaces

We prove that a polar foliation of codimension at least three in an irreducible compact symmetric space is hyperpolar, unless the symmetric space has rank one. For reducible symmetric spaces of compact type, we derive decomposition results for polar foliations.     

Pontryagin Classes of Generalized Symmetric Spaces

The real characteristic Pontryagin classes of generalized symmetric spaces with simple compact principal Lie groups are calculated in this paper.     

关于不分明对称广义邻近空间的性质(英文)

关于不分明邻近空间的概念是由A .K .Katsaras给出的 ,本文在此基础上 ,首先引入了不分明对称广义邻近空间的概念 .然后研究了不分明对称广义邻近空间的性质 .最后给出了不分明对称广义邻近空间的乘积性和邻近连续性 .     

Geometric Structures over Four-Dimensional Generalized Symmetric Spaces

We classify Walker structures, self-dual and anti-self-dual metrics among the invariant metrics of four-dimensional generalized symmetric spaces.     

极分解与广义*-Aluthge变换

首先给出了Hilbert空间上有界线性算子极分解的的若干性质.其次指出广义的*-Aluthge变换与*-Aluthge变换具有许多相似性质;例如,T_(α,β)^((*))=U|T_(α,β)((*))=U|T_(α,β)^((*))|当且仅当T是双正规的,即[|T|,|T*|]=0,其中对任意两个算子A和B,[A,B]=AB-BA.     

Interpolation of Operators on Scales of Generalized Lorentz-Zygmund Spaces

We define generalized Lorentz-Zygmund spaces and obtain interpolation theorems for quasilinear operators on such spaces, using weighted Hardy inequalities. In the limiting cases of interpolation, we discover certain scaling property of these spaces and use it to obtain fine interpolation theorems in which the source is a sum of spaces and the target is an intersection of spaces. This yields a considerable improvement of the known results which we demonstrate with examples. We prove sharpness of the interpolation theorems by showing that the constraints on parameters are necessary for the interpolation theorems.     

Some New Perturbation Bounds for the Generalized Polar Decomposition

The changes in the unitary polar factor under both multiplicative and additive perturbation are studied. A multiplicative perturbation bound and a new additive perturbation bound, in which a different measure of perturbation is introduced, are presented.     

A Characterization of Higher Rank Symmetric Spaces Via Bounded Cohomology

Let M be complete nonpositively curved Riemannian manifold of finite volume whose fundamental group Γ does not contain a finite index subgroup which is a product of infinite groups. We show that the universal cover is a higher rank symmetric space iff is injective (and otherwise the kernel is infinite dimensional). This is the converse of a theorem of Burger–Monod. The proof uses the celebrated Rank Rigidity Theorem, as well as a new construction of quasi-homomorphisms on groups that act on CAT(0) spaces and contain rank 1 elements. Received: September 2007, Accepted: March 2008     

一类广义插值在LM^Ba空间中的逼近

先引入了由一列Orlicz空间生成的Ba空间(LMBa)的定义,然后用分数阶α的连续模给出一类广义插值在LBMa空间中逼近阶.     

Real Interpolation of Generalized Besov-Hardy Spaces and Applications

In this paper we consider generalized Hardy spaces which include classical Hardy spaces and Hardy-Lorentz spaces as special cases. We give real interpolation results for such spaces. As applications, we solve an interpolation problem for Besov spaces of generalized smoothness and prove the boundedness of pseudodifferential operators acting both in these spaces and in the local Hardy spaces. For the latter spaces, we also obtain wavelet decompositions.     

一类广义插值在LBaM空间中的逼近

先引入了由一列Orlicz空间生成的Ba空间(LBaM)的定义,然后用分数阶α的连续模给出一类广义插值在LBaM空间中逼近阶.     

Generalized Interpolation in Bergman Spaces and Extremal Functions

In a recent paper A. Schuster and K. Seip [SchS] have characterized interpolating sequences for Bergman spaces in terms of extremal functions (or canonical divisors). As these are natural analogues in Bergman spaces of Blaschke products, this yields a Carleson type condition for interpolation. We intend to generalize this idea to generalized free interpolation in weighted Bergman spaces B^{p, α} as was done by V. Vasyunin [Va1] and N. Nikolski [Ni1] (cf.also [Ha2]) in the case of Hardy spaces. In particular we get a strong necessary condition for free interpolation in B^{p, α} on zero–sets of B^{p, α}–functions that in the special case of finite unions of B^{p, α}–interpolating sequences turns out to be also sufficient.     

Four-Dimensional Pseudo-Riemannian Generalized Symmetric Spaces Which are Algebraic Ricci Solitons

We classify, up to isometry, non-symmetric simply-connected four-dimensional pseudo-Riemannian generalized symmetric spaces which are algebraic Ricci solitons. It turns out that those of Cerny–Kowalski’s types A, C and D are algebraic Ricci solitons, whereas those of type B are not. Thus, we give new examples of algebraic Ricci solitons.     

Boundary Relations and Generalized Resolvents of Symmetric Operators in Krein Spaces

The classical Krein-Naimark formula establishes a one-to-one correspondence between the generalized resolvents of a closed symmetric operator in a Hilbert space and the class of Nevanlinna families in a parameter space. Recently it was shown by V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo that these parameter families can be interpreted as so-called Weyl families of boundary relations, and a new proof of the Krein-Naimark formula in the Hilbert space setting was given with the help of a coupling method. The main objective of this paper is to adapt the notion of boundary relations and their Weyl families to the Krein space case and to prove some variants of the Krein-Naimark formula in an indefinite setting.      

基于对称化原理的对称区域分裂法

本文利用对称化原理,讨论了一种只需在子区域上计算两个完全独立子问题就可得到原问题解的对称区域分裂法,并用此方法求解线性算子方程和线性透射问题.此方法可作为并行算法在MIMD计算机上使用.     

Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications

We study generalized polar decompositions of densely defined closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators. Based upon work partially supported by the US National Science Foundation under Grant Nos. DMS-0400639 and FRG-0456306, and the Austrian Science Fund (FWF) under Grant No. Y330.     

极空间的注记

本文中我们提到的极空间的秩不必是有限的。得到的主要结果是，令S是一个不可约的极空间，如果p～q，p～q是S中的点，则有极空间是同构的，我们把它记作