Radon Transform on Sobolev Spaces

Siberian Mathematical Journal - The Radon transform  $ R $ maps a function  $ f $ on  $ {??}^{n} $ to the family of the integrals of  $ f $ over...     

Banach Spaces which are Radon Spaces with the Weak Topology

In this paper, Schachermayer's Theorem [6] is improved by showingthat a WCG Banach space whose density is of measure zero isa Radon space with the weak topology (weak-Radon). We also considerother conditions under which a Banach space is a weak-Radonspace.     

Cauchy Complete Nearness Spaces

A nearness space is Cauchy complete if every regular Cauchy filter on the space is convergent. We show that the category CCNear ₂ of Cauchy complete N ₂ spaces is reflective in the category Near ₂ C of N ₂-spaces and Cauchy maps and that the reflection of an N ₂-space is given by the strict extension associated with regular Cauchy filters on the space.     

Distributions and Analytical Measures on Infinite-Dimensional Spaces

Spaces of test functions and spaces of distributions (generalized measures) on infinite-dimensional spaces are constructed, which, in the finite-dimensional case, coincide with classical spaces \(\mathscr{D}\) and \(\mathscr{D}'\). These distribution spaces contain generalized Feynman measures (but do not contain a generalized Lebesgue measure, which is not considered in this paper). For broad classes of infinite-dimensional differential equations in distribution spaces, the Cauchy problem has fundamental solutions. These results are much more definitive than those of A.Yu. Khrennikov’s and A.V. Uglanov’s pioneering works.     

无限状态空间上的测度和鞅

建立无限状态空间上的Radon－Nikodym定理和Riesz表示定理，引进测度值鞅并应用于超过程．     

完备和紧度量空间中的不动点

利用实函数性质,建立了两类度量空间中的几个不动点定理,推广了Fisher的有关定理。     

A Complete Real-Variable Theory of Hardy Spaces on Spaces of Homogeneous Type

Journal of Fourier Analysis and Applications - Let $$(X,d,\mu )$$ be a space of homogeneous type, with the upper dimension $$\omega $$ , in the sense of Coifman and Weiss. Assume that $$\eta $$ is...     

Stationary Random Measures on Homogeneous Spaces

This paper discusses stationary random measures on a homogeneous space and their Palm measures. It starts with such fundamental properties as the refined Campbell theorem and then proceeds to consider invariant transports, invariance and transport properties of Palm measures, and stationary partitions. A key tool is a transformation of random measures that permits the extension of recent results for stationary random measures on a group to the more general case of stationary random measures on a homogeneous state space.     

Lines,Trees, and Branch Spaces

In this paper we examine the interactions between the topology of certain linearly ordered topological spaces (LOTS) and the properties of trees in whose branch spaces they embed. As one example of the interaction between ordered spaces and trees, we characterize hereditary ultraparacompactness in a LOTS (or GO-space) X in terms of the possibility of embedding the space X in the branch space of a certain kind of tree.     

Spaces Universal under Closed Embeddings for Finite-Dimensional Complete Metric Spaces

We shall prove that for every natural number n and every cardinalnumber there exists an n-dimensional complete metric spaceX_n, of weight such that every n-dimensional complete metricspace of weight is embeddable in X_n, as a closed subset.     

σ - Complete Fuzzy Riesz Spaces

We define σ-complete fuzzy Riesz spaces and then study some of their interesting properties.     

完备度量空间中的混沌判定

本文研究完备度量空间上的离散动力系统的混沌标准,证明了如果完备度量空间X上的连续映射f具有正则非退化返回排斥子或连接不动点的正则非退化异宿环,则存在f的不变闭子集A,使得f限制在此不变闭子集上的子系统与两个符号的符号动力系统拓扑共轭,从而获得具有这类结构的连续映射f具有Devaney混沌、分布混沌、正拓扑熵及ω-混沌,...     

Complete Nevanlinna-Pick Property of Dirichlet-Type Spaces

We prove that all Dirichlet-type spaces of functions analytic in the unit disk whose derivatives are square area integrable with superharmonic weights have complete Nevanlinna-Pick reproducing kernels. As a corollary, we obtain a commutant lifting theorem for cyclic analytic two-isometries.     

Lacunary Measures and Self-similar Probability Measures in Function Spaces

The paper deals with multifractal quantities for some types of Radon measures,especiallyself-similar probability measures,and their relations to Besov spaces.     

Operator Semi-Selfdecomposable Measures and Related Nested Subclasses of Measures on Vector Spaces

T-semi-selfdecomposability, operator selfdecomposability, and subclasses L_m(b, (T_t)) and of measures on complete separable metric vector spaces are introduced and basic properties are proved. In particular, we show that is T-semi-selfdecomposable if and only if =T() where is infinitely divisible and is operator selfdecomposable if and only if L₀(b, (T_t)) for all 0<b<.