Comprehensive study of real analysis and functional analysis

实分析与泛函分析综合研究

基本信息

批准号：
05302008
负责人：
HIRAI Takeshi
金额：
$ 13.76万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-05302008/
关键词：
real analysis functional analysis function space representation operator algebra function algebra harmonic analysis partial differential equation 表現論

项目摘要

Our studies were mainly carried out according to the following five groups : Real Analysis and Commutative Harmonic Analysis, Function Spaces and Operators, Group Representations and Non-commutative Harmonic Analysis, Operator Algebras and Function Algebras, Functional Analytic Studies on Partial Differential Equations. We pick up some of the works of our members. In the first group, Morrey Spaces, BMO spaces, Besov spaces and operators on them were studied. A.Miyachi studied the spaces defined by means of sharp max functions, and problems on extension of functions on a domain and those on products of functions. S.Igari et al.studied Banach spaces and Banach algebras.F.Takeo studied Hausdorff dimension of fractal sets. S.Oharu et al.studied semigroups of non-linear oparators coming from non-linear evolution equations. Concerning this subject, they obtained final results on non-linear perturbations of analytic semigroups, adjoint semigroups etc. In the third group, representation theories of infinite dimensional Lie groups and quantum groups were studied. The works of M.Kashiwara and those of M.Jinbo are remarkable. T.Oshima, T.Kobayashi, H.Yamashita et al.studied representations of semisimple Lie groups and harmonic analysis on semisimple symmetric spaces. T.Hirai studied the construction of irreducible unitary representations of infinite discrete groups and the decomposition of their regular representations, and further Howe type duality between the infinite symmetric group and groups of diffeomorphisms on manifolds. Representations of Lie super-algebras were studied by K.Nishiyama et al.For partial differential equations, construction and expression of their solutions were studied by T.Kawai et al.H.Komatsu showde that his abstract Laplace transform can be applied to get rapidly the classical expression of the solutions of some explicit differential equations.

我们的研究主要根据以下五个组进行：实际分析和交换性谐波分析，功能空间和运算符，组表示和非交通谐波分析，运营商代数和功能代数，对部分微分方程的功能分析研究。我们拿起成员的一些作品。在第一组中，研究了Morrey空间，BMO空间，BESOV空间和操作员。 A.Miyachi研究了通过尖锐的最大函数定义的空间，以及在域上扩展功能和功能产品的空间。 S.Igari等人研究了Banach空间和Banach代数。F。Takeo研究了分形组的Hausdorff尺寸。 S.Oharu等人来自非线性进化方程的非线性渗透剂的半群。关于这一主题，他们在第三组的分析半群，伴随半群等的非线性扰动方面获得了最终结果，研究了无限尺寸谎言组和量子组的表示理论。 M.Kashiwara和M.Jinbo的作品非常出色。 T. oshima，T.Kobayashi，H.Yamashita等人的半神经谎言组的描述和半圣对称空间的谐波分析。 T.Hirai研究了无限离散组的不可约合统一表示的构建以及其常规表示的分解，并进一步构建了无限对称组与流形的差异群之间的二元性。 K.Nishiyama等人研究了谎言超晶状体的表示，以部分微分方程，T.Kawai等人的溶液的构建和表达，T.Kawai et al.H.Komatsu表明他的抽象拉普拉斯变换可快速地获得某些显性差分公式的解决方案的经典表达。