w-Frchet可微性质和Radon-Nikod(?)m性质以及w-Asplund空间

我们称定义在一个Banach空间的对偶空间上的广义实值w*-下半连续凸函数f具有w*-Frechet可微性质(w*-FDP),如果对于该对偶空间上的每个w*-下半连续的广义实值凸函数g,只要g≤f,就有g在intdom g的某个稠密的Gδ-子集上处处Frechet可微.本文用集合的Radon-Nikodym性质刻划了该种函数的特征.作为它的一个直接推论,给出了局部化的Collier定理.     

w-Frchet可微性质和Radon-Nikod(?)m性质以及w-Asplund空间

我们称定义在一个Banach空间的对偶空间上的广义实值w*-下半连续凸函数f具有w*-Frechet可微性质(w*-FDP),如果对于该对偶空间上的每个w*-下半连续的广义实值凸函数g,只要g≤f,就有g在intdom g的某个稠密的Gδ-子集上处处Frechet可微.本文用集合的Radon-Nikodym性质刻划了该种函数的特征.作为它的一个直接推论,给出了局部化的Collier定理.     

w*-Fréchet可微性质和Radon-Nikodym性质以及w*-Asplund空间

我们称定义在一个Banach空间的对偶空间上的广义实值w*-下半连续凸函数f具有w*-Fréchet可微性质(w*-FDP),如果对于该对偶空间上的每个w*-下半连续的广义实值凸函数g,只要g≤f,就有g在intdom g的某个稠密的Gδ-子集上处处Fréchet可微.本文用集合的Radon-Nikodym性质刻划了该种函数的特征.作为它的一个直接推论,给出了局部化的Collier定理.     

局部可分度量空间的伪序列覆盖映射

指出了文[1]中的一个问题,并给出了局部可分度量空间的伪序列覆盖s映象和局部可分度量空间的伪序列覆盖紧映象的刻划。     

局部可分度量空间的序列覆盖s象

本文给出了局部可分度量空间的1序列覆盖s象,2序列覆盖s象,强序列覆盖s象,序列覆盖s象及子序列覆盖s象的内在刻划．从而使关于对度量空间的各类s象的内在刻划方面的研究更趋于完整．     

L─Fuzzy拓扑空间的局部连通性

文［１］曾在广义拓扑分子格中提出了一种连通性。本文在Ｌ—ｆｕｚｚｙ拓扑空间中给出了这种连通性的几种刻划，并引入了Ｌ—ｆｙｚｚｙ拓扑空间的局部连通性。这种局部连通性是有限可乘的，商序同态保持的且是好的推广。另外，ｆｕｚｚｙ实直线是局部连通的。     

关于Baskakov-Durrmeyer算子的局部逼近

本文主要讨论了用Ｈｏｌｄｅｒ连续函数表示Ｂａｓｋａｋｏｖ－Ｄｕｒｒｍｅｙｅｒ算子局部逼近阶的特征刻划问题。     

两指标局部鞅的停止变换及Wiener过程的鞅刻划

本文主要讨论两指标局部平方可积鞅的停止变换问题及Ｗｉｅｎｅｒ过程的鞅刻划和停止问题。     

L—Fuzzy拓扑空间的局部连通性

文（１）曾在广义拓扑分子格中提出了一种连通性。本文在Ｌ－ｆｕｚｚｙ拓扑空间中给出了这种连通性的几种刻划，并引入了Ｌ－ｆｕｚｚｙ拓扑空间的局部连通性，这种局部连通性是有限可乘的，商序同态保持的且是好的推广，另外，ｆｕｚｚｙ实直线是局部连通的。     

微分模式

１．论述ｄｘ与△ｘ的关系；ｄｘ是从△ｘ→０转化而来．比△ｘ更为抽象；２对多元函数引出几．种可微性概念，更加细致地刻划其可微性。     

Microlocal smoothing effect for the Schrödinger evolution equation in a Gevrey class

We discuss the microlocal Gevrey smoothing effect for the Schrödinger equation with variable coefficients via the propagation property of the wave front set of homogenous type. We apply the microlocal exponential estimates in a Gevrey case to prove our result.     

Morera theorems via microlocal analysis

We prove Morera theorems for curves in the plane using microlocal analysis. The key is that microlocal smoothness of functions is reflected by smoothness of their Morera integrals on curvestheir Radon transforms. Parallel support theorems for the associated Radon transforms follow from our arguments by a simple correspondence.     

Propagation des singularités Gevrey pour l’équation de Cauchy-Riemann dégénérée

In this paper we study the degenerate Cauchy-Riemann equation in Gevrey classes. We first prove the local solvability in Gevrey classes of functions and ultra-distributions. Using microlocal techniques with Fourier integral operators of infinite order and microlocal energy estimates, we prove a result of propagation of singularities along one dimensional bicharacteristics.      

On the sensitivity of solutions of hyperbolic

The goal of this work is to determine appropriate domain and range of the map from the coefficients to the solutions of the wave equation for which its linearization or formal derivative is bounded and the properties of the coefficients on which the bound depends.Such information is indispensable in the study of the inverse (coefficient identification) problem vio smooth optimization methods. The main result of this paper is an explicit microlocal Sobolev estimate for the linearized forward map. In view of results of Rakesh [19] for the smooth coefficient case, the order of our regularity result is optimal. Our proof is based on the method of nonsmooth microlocal analysis, in particular various results on propagation of singularities, the method of progressing wave expansions, microlocal study of solutions of the transport equations, study of conormal properties of the fundamental solution, and a duality technique.     

Propagation of singularities in Cauchy problems for quasilinear thermoelastic systems in three space variables

By using microlocal analysis, the propagation of weak singularities in Cauchy problems for quasilinear thermoelastic systems in three space variables are investigated. First, paradifferential operators are employed to decouple the quasilinear thermoelastic systems. Second, by investigating the decoupled hyperbolic-parabolic systems and using the classical bootstrap argument, the property of finite propagation speeds of singularities in Cauchy problems for the quasilinear thermoelastic systems is obtained. Finally, it is shown that the microlocal weak singularities for Cauchy problems of the thermoelastic systems are propagated along the null bicharacteristics of the hyperbolic operators.     

Regularity, Local and Microlocal Analysis in Theories of Generalized Functions

We introduce a general context involving a presheaf and a subpresheaf ℬ of  . We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic techniques) can be interpretated as the ℬ-local analysis of sections of  . But the microlocal analysis of the sections of sheaves or presheaves under consideration is dissociated into a “frequential microlocal analysis” and into a “microlocal asymptotic analysis”. The frequential microlocal analysis based on the Fourier transform leads to the study of propagation of singularities under only linear (including pseudodifferential) operators in the theories described here, but has been extended to some non linear cases in classical theories involving Sobolev techniques. The microlocal asymptotic analysis is a new spectral study of singularities. It can inherit from the algebraic structure of ℬ some good properties with respect to nonlinear operations.      

Analyse de l'espace des phases et calcul pseudo-differential sur le groupe de Heisenberg

We establish pseudo-differential calculus on the Heisenberg group by defining an algebra of operators acting continuously on Sobolev spaces and containing the class of differential operators. Our approach puts into light microlocal directions and completes, with the Littlewood–Paley theory developed by Bahouri et al., a microlocal analysis of the Heisenberg group. To cite this article: H. Bahouri et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Quasihomogeneous Gevrey wave front and iterates of differential operators

We give a microlocal version of the theorem of the iterates for quasihomogeneous hypoelliptic operators in anisotropic Gevrey spaces.     

A Characterization for the Gevrey-Sobolev Wave Front Set

In this note, we use the so-called microlocal energy method to give a characterization of the Gevrey-Sobolev wave front set , which will be useful in the study of non-linear microlocal analysis in Gevrey classes. Research supported by grants of the Natural Science Foundation of China, the State Education Committee and the Huacheng Foundation.     

On the Microlocal Properties of the Range of Systems of Principal Type

The purpose of this paper is to study microlocal conditions for inclusion relations between the ranges of square systems of pseudodifferential operators which fail to be locally solvable. The work is an extension of earlier results for the scalar case in this direction, where analogues of results by L. Hörmander about inclusion relations between the ranges of first order differential operators with coefficients in C ^∞ which fail to be locally solvable were obtained. We shall study the properties of the range of systems of principal type with constant characteristics for which condition (Ψ) is known to be equivalent to microlocal solvability.