Research on families of functions determining structures of spaces of analytic functions

决定解析函数空间结构的函数族研究

基本信息

批准号：
10440039
负责人：
IZUCHI Keiji
金额：
$ 5.82万
依托单位：
NIIGATA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

Izuchi (Head investigator) introduced the concept of weak infinite powers of Blaschke products and characterized Blaschke products which are weak generators of L^∞. Also Izuchi defined L^1 and L^∞-type singular inner functions and showed that for a positive singular measure there exists a particular set in M (H^∞) associated with the measure. He proved the existence of trivial points which are not contained in the closure of a nontrivial Gleason part. This answers the Budde problem. And the set of such points is dense in the set of trivial points.Izuchi showed the existence of homeomorphic parts which are not locally sparse. This answers Gorkin-Mortini problem. He determined closed ideals of H^∞ whose zero sets are contained in the set of nontrivial points (with Gorkin-Mortini). Also Izuchi solved the Gorkin-Mortini problem concerning with prime ideals in H^∞+C.About invariant subspaces on T^2, Izuchi studied A_φ-invariant subspaces and gen-eralized Nakazi's theorems (with Matsugu). And he started to study composition operators on H^∞ and determined connected components with respect to the essential norm topology (with Zheng).On the results of investigators, Saito determined invariant subspaces on T^2 under the certain condition. Huruya defined the concept of p-hyponormality for n-tuple operators, and proved Putnam type inequality. Hayashi showed that Myrberg phenomenon follows from the uniquness theorem under some additinal conditions. Hatori solved Lausen-Neumann's problem concerned with commutative Banach al-gebras. On a Bohr group, Tanaka proved that an invariant subspace generated by a single function if and only if its cocycle is cohomologous to a singular cocycle. Takagi studied multiplicative and composition operators on ^p-spaces.

Izuchi（负责人）介绍了Blaschke产品的弱无限力量的概念，并表征了Blaschke产品，这些blaschke产品是L^∞的弱发生器。 izuchi也定义了l^1和l^∞型奇异内部函数，并表明，对于正面的奇异测量，存在与测量相关的m（h^∞）中的特定集合。他证明了无处不在的无处不在格里森部分中没有包含的琐碎点。这回答了好友问题。这种点的集合在一组琐碎的地方很稠密。Izuchi显示出并非局部稀疏的同构部分的存在。这回答了Gorkin-Mortini问题。他确定了H^∞的封闭思想，其零集包含在非平凡点（带有Gorkin-Mortini）中。 Izuchi还解决了与H^∞+C.在T^2上不变子空间中的主要思想有关的Gorkin-Mortini问题，Izuchi研究了A_φ-Invariant子空间和Generalized Nakazi的Nakazi定理（带有Matsugu）。他开始研究H^∞的组成算子，并确定相对于基本规范拓扑（使用Zheng）的连接组件。关于研究人员的结果，锡托在特定条件下确定了T^2的不变子空间。 Huruya定义了N型培训机构的P--甲基词概念，并经过证明是Putnam Type不平等的概念。 Hayashi表明，Myrberg现象在某些添加剂条件下从Unices定理中遵循。 Hatori解决了Lausen-Neumann与交换性Banach al-Gebras有关的问题。在BOHR组上，田中证明了一个函数产生的不变子空间，并且仅当其Cocycle共同出现与奇异共生时。 takagi Studiod乘法和组成算子在 ^p空间上。