Hilbert空间中最终范数连续半群的特征条件

本文给出了Hilbert空间中当t>t0(t0≥0)时,按一致算子拓扑连续C0半 群T(t)的四个特征条件.     

A Continuous Kernel for the Transition Semigroup Associated with a Diffusion Process in a Hilbert Space

We give an explicit formula for the kernel of the semigroup determined by the solution of a stochastic semilinear equation, where the nonlinear part of the drift is the gradient of a function.     

Regular Densities of Invariant Measures in Hilbert Spaces

We consider a nonlinear differential stochastical equation in a Hilbert space, that is, a Lipschitzian perturbation of a linear equation. We prove that, under suitable hypotheses, both equations have invariant measures μ and μ₀ respectively and that μ is absolutely continuous with respect to μ₀. We also give several regularity results on the density dμ/dμ₀.     

On the Accuracy of Gaussian Approximation in Hilbert Space

The bound on remainder term in CLT for a sum of independent random variables taking values in Hilbert space is obtained. This bound sharpens the result due to Bentkus and Götze.     

Approximation of Surface Measures in a Locally Convex Space

The main result of the paper is an analog of the surface layer theorem for measures given on a locally convex space with a continuously and densely embedded Hilbert subspace (for a surface of finite codimension). Earlier, the surface layer theorem was proved only for Banach spaces: for surfaces of codimension 1 by Uglanov (1979) and for surfaces of an arbitrary finite codimension by Yakhlakov (1990). In these works, the definition of the surface layer and the proof of the theorem essentially use the fact that the original space is equipped with a norm.     

On the Properties of Some Class of Measures in a Hilbert Space

We find conditions for absolute continuity of transition probabilities of Markov processes in a Hilbert space.     

Hilbert空间中范数连续半群的特征

给出Hilbert空间中范数连续半群的一个新特征，同时极大地简化了已有结果的证明。     

Approximating a Feller Semigroup by Using the Yosida Approximation of the Symbol of its Generator

We show that if the pseudodifferential operator −q(x,D) generates a Feller semigroup (T_t)_t≥0 then the Feller semigroups (T_t^(v))_t≥0 generated by the pseudodifferential operators with symbol will converge strongly to (T_t)_t≥0 as ν →∞.     

Orlicz-Sobolev空间的Lipschitz连续函数逼近

对Orlicz-Sobolev空间的性质进行了深入的研究,Orlicz-Sobolev函数可用在开集外为零的Lipschitz连续函数来逼近,对解决微分方程问题起了很重要的作用.     

On a Continuous Third-Order Method for Monotone Operator Equations in Hilbert Space

A continuous third-order method has been constructed for a nonlinear operator equation in a Hilbert space with a strongly monotone operator satisfying the Lipshitz condition. Conditions sufficient for the strong convergence of the method have been derived.     

Approximate Identities in Spaces of all Absolutely Continuous Measures on Locally Compact Semigroups

Let G be a locally compact group. Then M_a (G), the space of all absolutely continuous measures on G, has a bounded approximate identity. Baker and Baker proved that (S) (the space of all measures M(S) so that maps x _x *|| and x ||*_x are weak continuous from a locally compact semigroup S into M(S)) is closed under absolutely continuity and has an approximate identity. The main purpose of this paper is to show that similar results hold true for a locally compact semigroup S and M_a(S) the space of all absolutely continuous measures on S.     

A Characterization of Strongly Continuous Groups of Linear Operators on a Hilbert Space

It is proved that the infinitesimal generator A of a stronglycontinuous semigroup of linear operators on a Hilbert spacealso generates a strongly continuous group if and only if theresolvent of –A, ( + A)^–1, is also a bounded functionon some right-hand-side half plane of complex numbers, and convergesstrongly to zero as the real part of tends to infinity. Anapplication to a partial differential equation is given. 1991Mathematics Subject Classification 47D03.     

Hilbert空间上最终范数连续半群的特征刻画

本文研究Hilbert空间上最终范数连续半群的特征条件,仅利用半群生成元的预解式,给出Hilbert空间上C0-半群最终范数连续的一个的充要条件.     

Algorithm for the Semigroup of a Space Curve Singularity

The semigroup of values of irreducible space curve singularities is the set of intersection multiplicities among hypersurfaces and the given curve. It is an invariant of the singularity, and for plane curves it characterizes the equisingularity type considered by Zariski. For space curve singularities the semigroup of values is a numerical semigroup and it can not be computed by means of the exponents of any Puiseux parametrization, as in the plane case. We obtain an algorithm for calculating the semigroup of values of a space curve singularity, which determines the generators of the semigroup and the valuation ideals associated with the semigroup. We give a Maple version of the algorithm.     

On the Dirichlet semigroup for Ornstein-Uhlenbeck operators in subsets of Hilbert spaces

We consider a family of self-adjoint Ornstein-Uhlenbeck operators Lα in an infinite dimensional Hilbert space H having the same gaussian invariant measure μ for all α∈[0,1]. We study the Dirichlet problem for the equation λφ−Lαφ=f in a closed set K, with f∈L²(K,μ). We first prove that the variational solution, trivially provided by the Lax-Milgram theorem, can be represented, as expected, by means of the transition semigroup stopped to K. Then we address two problems: 1) the regularity of the solution φ (which is by definition in a Sobolev space ) of the Dirichlet problem; 2) the meaning of the Dirichlet boundary condition. Concerning regularity, we are able to prove interior regularity results; concerning the boundary condition we consider both irregular and regular boundaries. In the first case we content to have a solution whose null extension outside K belongs to . In the second case we exploit the Malliavin's theory of surface integrals which is recalled in Appendix A of the paper, then we are able to give a meaning to the trace of φ at ∂K and to show that it vanishes, as it is natural.     

Viscosity Approximation Methods for a Class of Generalized Split Feasibility Problems with Variational Inequalities in Hilbert Space

Strong convergence theorem of viscosity approximation methods for nonexpansive mapping have been studied. We also know that CQ algorithm for solving the split feasibility problem (SFP) has a weak convergence result. In this paper, we use viscosity approximation methods and some related knowledge to solve a class of generalized SFP’s with monotone variational inequalities in Hilbert space. We propose some iterative algorithms based on viscosity approximation methods and get strong convergence theorems. As applications, we can use algorithms we proposed for solving split variational inequality problems (SVIP), split constrained convex minimization problems and some related problems in Hilbert space.     

Hilbert空间中广义算子半群范数连续的特征

研究了Hilbert空间上最终范数连续广义算子半群的特征条件,利用半群的生成元的预解式,给出了Hilbert空间上广义算子半群范数连续的三个特征条件.     

Equivariant Embeddings of the n-Dimensional Space into a Hilbert Space

The present paper is devoted to the study of equivariant embeddings of the n-dimensional space into a Hilbert space. We consider a representation of a group of similarities. The existence of a cocycle for this representation implies the existence of an isometric embedding of a metric group into the Hilbert space. Then we describe all cocycles of a representation of the additive group of real numbers and construct an embedding of the n-dimensional space with metric d(x,y)=|x-y| into the Hilbert space. Bibliography: 5 titles.