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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

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10440039/
关键词：
Spaces of analytic functions bounded analytic function maximal ideal space Blaschke product singular inner function Gleason part invariant subspace Korovkin type theorem 有界解析関数環ダグラス環閉イデアルバナッハ環 BKW作用案コロフキンの定理

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（首席研究员）介绍了 Blaschke 积的弱无穷幂的概念，并描述了 Blaschke 积的特征，它是 L^∞ 的弱生成器。 Izuchi 还定义了 L^1 和 L^∞ 型奇异内函数，并表明对于正奇异测度，M (H^∞) 中存在与该测度相关的特定集合。他证明了存在不包含在非平凡格里森部分的闭包中的平凡点。这回答了布德问题。并且这些点的集合在琐碎点的集合中是稠密的。Izuchi证明了同胚部分的存在，它们不是局部稀疏的。这回答了戈尔金-莫蒂尼问题。他确定了 H^∞ 的闭合理想，其零集包含在非平凡点集中（与 Gorkin-Mortini 一起）。 Izuchi还解决了与H^∞+C中的素理想有关的Gorkin-Mortini问题。关于T^2上的不变子空间，Izuchi研究了A_φ不变子空间并推广了Nakazi定理（与Matsugu一起）。他开始研究H^∞上的复合算子，并确定关于本质范数拓扑的连通分量（与Zheng合作）。斋藤根据研究者的成果，在一定条件下确定了T^2上的不变子空间。 Huruya定义了n元组算子的p-次正规性概念，并证明了Putnam型不等式。 Hayashi 证明了米尔伯格现象在某些附加条件下遵循唯一性定理。 Hatori 解决了与交换巴纳赫代数有关的劳森-诺依曼问题。在玻尔群上，田中证明了由单个函数生成的不变子空间当且仅当其余循环与奇异余循环上同调。 Takagi 研究了 ^p 空间上的乘法和复合算子。