On the existence of Feller semigroups with discontinuous coefficients II

This paper is devoted to the functional analytic approach to the problem of existence of Markov processes with Dirichlet boundary condition, oblique derivative boundary condition and first-order Wentzell boundary condition for second-order, uniformly elliptic differential operators with discontinuous coefficients. More precisely, we construct Feller semigroups associated with absorption, reflection, drift and sticking phenomena at the boundary. The approach here is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the Calderon- Zygmund theory of singular integral operators with non-smooth kernels.     

On Gauss-Weierstrass semigroups and inversion of potentials associated with the Bessel differential operator

In this paper, we define the generalized Gauss Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potentials, generated by the generalized shift operators and associated with the Laplace Bessel differential operator.     

The heat semigroup and Brownian motion on strip complexes

We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing “strips” along their natural boundaries according to a given graph structure. The most familiar example is the one-dimensional complex classically associated with a graph, in which case the strips are simply copies of the unit interval (our setup actually allows for variable edge length). A leading key example is treebolic space, a geometric object studied in a number of recent articles, which arises as a horocyclic product of a metric tree with the hyperbolic plane. In this case, the graph is a regular tree, the strips are [0,1]×R, and each strip is equipped with the hyperbolic geometry of a specific strip in upper half plane. We consider natural families of Dirichlet forms on a general strip complex and show that the associated heat kernels and harmonic functions have very strong smoothness properties. We study questions such as essential self-adjointness of the underlying differential operator acting on a suitable space of smooth functions satisfying a Kirchhoff type condition at points where the strip complex bifurcates. Compatibility with projections that arise from proper group actions is also considered.     

全变换半群的极大半传递幺半群(英文)

对任一个非空集X,X上的全变换半群T(X)的一个子幺半群M被称为半传递,如果M为非传递,且对每个序对(x,y)∈X×X,存在∈M使x=y或y=x.本文刻画了全变换半群T(X)的所有极大半传递子幺半群;对T(X)的每个极大半传递子幺半群M,相关秩r(T(X),M)被证明为1.对有限集X,给出T(X)的极大半传递子幺半群的个数,且T(X)的最大基数的半传递子幺半群被刻画.     

Ornstein-Uhlenbeck半群证明不等式的一些应用

按照Ornstein-Uhlenbeck的思想方法,用Ornstein-Uhlenbeck半群和Ornstein-Uhlenbeck算子的一些重要性质,对Brascamp-Lieb不等式、高斯对数Sobolev不等式、逆Bobkov等周不等式等几个重要的几何与分析不等式给出了另一证明.     

<Emphasis Type="Italic">hĥ</Emphasis>-transforms of positivity preserving semigroups and associated Markov processes

The hĥ--transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hĥ--associated with a pair of special standard processes which are in weak duality.     

Admissibility and Observability of Observation Operators for Semilinear Problems

This paper deals with semilinear evolution equations with unbounded observation operators. Sufficient conditions are given guaranteeing that the output function of a semilinear system is in L²_loc([0, ∞); Y). We prove that the Lebesgue extension of the observation operators are invariant under nonlinear globally Lipschitz continuous perturbations. Further, relations between the corresponding -extensions are studied. We show that exact observability of linear autonomous system is conserved under small Lipschitz perturbations. The obtained results are illustrated by several examples.      

一类具有可修故障和不可修故障的两部件并联可修系统的适定性问题

主要用强连续半群理论,研究了一类具有可修故障和不可修故障的两部件并联系统非负时间依赖解的存在惟一性问题.     

具有逆断面的局部逆半群

Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.     

Eventual norm continuity for neutral semigroups on Banach spaces

In this paper we prove, under suitable hypotheses, eventually norm continuity and compactness of the solution semigroups of certain neutral differential equations in Banach spaces. Our approach is based on a general perturbation theorem obtained from closed-loop systems of infinite dimensional control systems with unbounded control and observation operators. In fact, the solution semigroup can be viewed as the semigroup of an appropriate closed-loop system in product state spaces.