Functional Analyistic Studies On The Algebra Of Bounded Analytic Functions On A Riemann Surface

黎曼曲面上有界解析函数代数的泛函分析研究

• 批准号: 16540132
• 负责人: HAYASHI Mikihiro
• 金额: $ 2.48万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16540132/
• 关键词: bounded analytic function; maximal ideal space; Riemann surface; pole set; Shilov boundary; Hardy class; composition operator; invariant subspace; 補間問題; 同型問題; pole集合

1. Studies on Riemann surfaces and bounded analytic functions and harmonic functions on them:In the case that a given Riemann surface is not included openly and homeomorphically in the maximal ideal space of the algebra of all bounded analytic functions, we find a condition on a Riemann surface whose Shilov boundary is totally disconeccted. This result can be applied to the uniqueness theorem of linear extremal problem. Also, we studied the structure of the fibre in the maximal ideal space. In addition, we show that Royden's resolution of a Riemann surface can be constructed by the method of simultaneous analytic continuation of a give family of meromorphic functions.We studied on relations between the Martin boundary and harmonic functions. We succeeded in a characterization for the existence of Green functions on a infinite-sheeted covering Riemann surface over the Riemann sphere, that is obtained by pasting a pair of sheets along each curve in a given sequence of curves, in terms of the sequence of capacities of curves.2. Stuies on Hardy classes and the function theory of several variables:We give the best possible estimate of the norm of cross-commutators of two subnormal operators by means of spectral area, and generalized a former result to the case of p-quasi normal operators.We give a characterization of weighted Herz space by means of wavelets. Our result correct an error in the result published by Tang-Yang in 2000, and further showed that our system of wavelets form an unconditional basis.We gave a new type of factorization of an inner function in relation of connected components of the zero of the inner function, which solves a problem posed in a paper published in 2004. We also studies when a linear combination of composition operators is compact for an analytic function space.

1。对Riemann表面和有界的分析功能和谐波功能的研究：如果给定的Riemann表面并未在所有有界分析函数的代数的最大理想空间中公开和同义，那么我们在Riemann表面上发现其完全分离的Riemann表面上的条件。该结果可以应用于线性极端问题的唯一定理。另外，我们研究了最大理想空间中纤维的结构。此外，我们表明罗伊登（Royden）可以通过同时分析延续的方法来构建罗伊登（Royden）对riemann表面的分辨率，从而使Meromorormorphic函数家族始终进行。我们研究了Martin边界和谐波功能之间的关系。我们成功地表征了在riemann球体上覆盖riemann表面的无限层面上存在绿色函数的表征，这是通过曲线的能力序列以给定曲线沿每个曲线沿每个曲线粘贴一对曲线来获得的。2。关于强硬类和几个变量的功能理论的说法：我们通过光谱区域对两个亚正常运算符的交叉交易者的规范进行了最佳估计，并通过波波通过小波来表征加权HERZ空间。我们的结果纠正了Tang-Yang在2000年发表的结果中的错误，进一步表明我们的小波系统形成了无条件的基础。我们给出了内部功能的新类型的内部分解，与内部功能的零相互关联组件相关，该问题解决了在2004年发表的论文中构成的问题。我们还研究了在2004年发表的研究。我们还研究了构成型启动的线性组合功能时，我们还研究了一个分析的效果。

项目成果

Double commuting compresset shifts and generalized interpolation in the Hardy space over the bidisc

Bidisc 上的 Hardy 空间中的双通勤压缩组移位和广义插值

• 发表时间: 2006
• 期刊: Integr. equ. oper. theory 56
• 作者: Hayashi;Susumu;T.Nakazi
• 通讯作者: T.Nakazi

Backward shift invariant subspaces in the bidisc

• DOI: 10.14492/hokmj/1285766003
• 发表时间: 2000-10

Isometric composition operators between two weighted hardy spaces

两个加权 Hardy 空间之间的等距合成运算符

• 发表时间: 2006
• 期刊: Nihonkai Math. J. 17
• 作者: 中路 貴彦;瀬戸 道生
• 通讯作者: 瀬戸 道生

Hyperbolic Riemann surfaces without unbounded positive haromic functions

没有无界正调和函数的双曲黎曼曲面

• 发表时间: 2006
• 期刊: Advanced Studies in Pure Math. 44
• 作者: Masaoka;H.
• 通讯作者: H.

Factorizations of functions in H^p(T^n)

H^p(T^n) 中函数的因式分解

• 发表时间: 2004
• 期刊: Complex Variables. Theory and Application. An International Journal 49
• 作者: Hosokawa;Takuya;Kei Ji Izuchi;Akihiko Inoue;Kei Ji Izuchi;Kei Ji Izuchi;KeiJi Izuchi;Keiji Izuchi;Osamu Hatori;Takahiko Nakazi;Takahiko Nakazi;Takahiko Nakazi;Keiji Izuchi;林 実樹廣;Takahiko Nakazi
• 通讯作者: Takahiko Nakazi