闭集值测度Radon—Nikodym导数的存在性

本文讨论可分Ｂａｎａｃｈ空间上闭集值测度Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ导数的存在性。     

RP—环

本文定义了ＲＰ－环,讨论了它的性质和等价条件,得出了Ｓ＝Ｍｎ（Ｒ）是ＲＰ－环妥且仅当Ｒ是ＲＰ－环;Ｒｉ是ＲＰ－环当且仅当每个Ｒｉ是ＲＰ－环．最后讨论了ＲＰ－环的同态象和左投射维数．     

关于Fejer—Riesz不等式

本文给出（ｉ）一个Ｆｅｊｅｒ－Ｒｉｅｓｚ定理的改进;（ｉｉ）一种Ｆｅｊｅｒ－Ｒｉｅｓｚ定理的推广（在ＨＰ函数空间上）     

闭集值测度Radon－Nikodym导数的存在性

本文讨论了可分Ｂａｎａｃｈ空间上闭集值测度Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ导数的存在性．     

CO—s闭拓扑

本文证明，当空间赋予ＣＯ－ｓ－闭石扑ｓ（τ）时，ｓ－连续函数概念与连续函数概念一致，研究了ｓ－ｘ闭空间；ｓ－闭空间的某些基本性质，且用其刻画几类ＣＯ－ｓ闭拓扑。     

无限状态空间上的Radon—Nikodym性质（Ⅰ）

利用有界变差向量测定空间给出一个Ｂａｎａｃｈ空间有Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的内蕴几何刻划，所用工具为本文进行的向量测试值鞅。     

一些新的多重Rogers—Ramanujan恒等式

本文利用初等方法简捷地推了Ｐａｕｌｅ的结果，从而得到了一系列多重Ｒｏｇｅｒｓ－Ｒａｍａｎｕｊａｎ恒等式。     

PC—环与几乎优越扩张

本文我们讨论了这种环R的结构,R是凝聚环且R作为R－模是P－内射,我们称此环为PC－环,并证明了在几乎优越扩张下的不变性。     

Ω—场的暴涨宇宙

本主旨在应用余Ｓｈｅｎ提出的Ω－场理论，去研究宇宙学问题。假设时空遵从罗伯逊－沃尔克（Ｒ－Ｗ）度规的结构，而能量张量动量张量只包含Ω－场的项，我们证明宇宙早期存在一急速暴涨阶段。视界问题和平直性问题从而获得则自然的解释。     

Sequential density techniques for an approximate Radon-Nikodým theorem

We deal with the problem of approximate representation of linear functionals and show how the sequential density techniques may be used for solution.     

Characterization of Multidimensional Stable Random Measures by Means of Vector Measures

Abstract

In connection with a symmetric α stable random measure Φ on a measurable space (F, ?) with values in R ^d , a complete metric space of symmetric finite measures on S _d?1 is constructed, and is employed to characterize the law of Φ by a unique positive measure on ? and a unique function on F × R ^d . The stochastic integral ∫ _F f d Φ is also defined for certain d × d matrix valued functions f, which for α = 2 reduces to the Wiener–Masani integral.     

Concerning Nikodym-type sets in 3-dimensional curved spaces

We investigate maximal functions involving averages over geodesics in three-dimensional Riemannian manifolds. We first show that one can easily extend the Euclidean results of Bourgain and Wolff if one assumes constant curvature. These results need not hold if this assumption is dropped. Nonetheless, we formulate a generic geometric condition which allows favorable estimates. Curiously, this condition ensures that one is in some sense as far as possible from the constant curvature case. Assuming this, one can prove dimensional estimates for Nikodym-type sets which are essentially optimal. Optimal estimates for the related maximal functions are still open though.

     

Two versions of the Nikodym maximal function on the Heisenberg group

The classical Nikodym maximal function on the Euclidean plane R² is defined as the supremum over averages over rectangles of eccentricity N; its operator norm in L²(R²) is known to be O(logN). We consider two variants, one on the standard Heisenberg group H¹ and the other on the polarized Heisenberg group . The latter has logarithmic L² operator norm, while the former has the L² operator norm which grows essentially of order O(N1/4). We shall imbed these two maximal operators in the family of operators associated to the hypersurfaces {(x₁,x₂,αx₁x₂)} in the Heisenberg group H¹ where the exceptional blow up in N occurs when α=0.     

Fixed point property and normal structure for Banach spaces associated to locally compact groups

In this paper we investigate when various Banach spaces associated to a locally compact group have the fixed point property for nonexpansive mappings or normal structure. We give sufficient conditions and some necessary conditions about for the Fourier and Fourier-Stieltjes algebras to have the fixed point property. We also show that if a -algebra has the fixed point property then for any normal element of , the spectrum is countable and that the group -algebra has weak normal structure if and only if is finite.