Weak convergence of positive vector measures with applications to real analysis

正向量测量与实际分析应用的收敛性较弱

基本信息

批准号：
13640162
负责人：
KAWABE Jun
金额：
$ 2.05万
依托单位：
SHINSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

项目摘要

We have studied weak convergence of positive vector measures with values in Banach spaces and nuclear spaces, and have applied to several interesting problems in real analysis, probability theory, control theory, differential geometry and so on. Some of our important results are as follows:1. A sequential compactness criterion is given for the weak topology of vector measures with values in certain nuclear spaces.2. It is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to the weak convergence of vector measures. Our approach to this problem is based on Bartle's bilinear integration theory.3. Prokhorov-LeCam' s compactness criteria and Varadarajan' s metrizability criterion are given for vector measures with values in Frechet spaces, semi-reflexive spaces, and semi-Montel spaces.4. The existence and uniqueness of the Borel injective tensor product of two Banach space-valued vector measures and the validity … More of a Fubini-type theorem are shown. Thanks to these results, the convolution of vector measures on a topological semigroup is defined as the measure induced by their Borel injective tensor product and the semigroup operation. The joint weak continuity of Borel injective tensor products or convolutions of vector measures is also proved.5. Compactness and sequential compactness criteria are given for a set of vector measures on a complete separable metric space with values in a certain semi-Montel space.6. It is shown that the Portmanteau Theorem remains valid for order σ-additive, positive vector measures with values in a Dedekind σ-complete Riesz space.7. A general theorem for the method of absolute Norulund summability is given.8. Some new characterizations of compact sets are given.9. The uniqueness of the solutions in H^∞ control problems is proved for general plants. Another proof, which does not depend on the complexity of the form of the algebraic Riccati equations, is also given.10. It is proved that there is a qubic-free sequence of letters.11. It is shown that a conformal Killing vector field is parallel on a compact almost Kahlerian manifold. Less

我们已经研究了阳性矢量测量与Banach空间和核空间中的值的弱收敛性，并应用于实际分析，概率理论，控制理论，差异几何形状等的几个有趣问题。我们的一些重要结果如下：1。对于在某些核空间中的值的较弱的矢量测量拓扑，给出了顺序的紧凑标准。2。结果表明，与矢量测量的弱收敛性相对于某些BANACH晶格中阳性矢量测量的启动量量是共同的。我们解决这个问题的方法是基于Bartle的双线性整合理论3。 Prokhorov-Lecam的紧凑标准和Varadarajan的度量标准用于矢量测量值，其值是在Frechet空间，半反射空间和半蒙难空间中的值。4。显示了两个Banach空间值矢量测量和有效性的borel Injementive张量产物的存在和独特性……更多的fubini-Type定理。感谢这些结果，拓扑半群上的向量测量值定义为由其Borel注射量张量产品和半群操作引起的测量。还证明了Borel注射量张量产物或向量测量的卷积的关节弱连续性。5。在完整的单独的度量空间上，给出了一组矢量测量值的紧凑度和顺序紧凑标准，该矢量测量值在某个半蒙太德空间中具有值。6。结果表明，portmanteau定理对于σ加addive，正载向量测量的阶数仍然有效。给出了绝对Norulund总结方法的一般理论。8。给出了一些紧凑型集的新字符。9。 H^∞控制问题的独特性证明了通用植物的唯一性。还给出了另一个证据，不取决于代数riccati方程的复杂性。10。事实证明，有一个无Qubic的字母序列。11。结果表明，在紧凑的几乎是卡勒利亚的歧管上，保形杀死矢量场是平行的。较少的