Studies of Harmonic Analysis

谐波分析研究

• 批准号: 60460003
• 负责人: IGARI Satoru
• 金额: $ 4.16万
• 依托单位: TOHOKU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-60460003/
• 关键词: Harmonic function; subharmonic function; Hardy space; Operator algebra; Evolution equation; Semi-simple group; D-module; 補間定理

Classical harmonic analysis has been a considerable flowering duaring the past 15 years starting from the results due to Fefferman-Stein,Carleson and others. The object of our program was to study the idea of classical harmonic analysis and to develop it in various fields in mathematics by the coorperative research with several specialists in our institute.An extract of our results is the following :1. An interpolation theorem of operators on a product measure space is shown. As applications we solved partially a problem on Riesz-Bochner means and on Kakeya's maximal function. Hardy spaces on a product space are investigated with connection to holomorphic functions of two variables.We are now generalizing classical Hardy space theory to a manifold of negative curvature.2. We have studied non-linear evolution equations getting several results on a property of the solutions of Navier-Stokes equation near t = 0, existence of global solutions and analiticity of solutions.3. By a method of D-modules it is succeeded to analyse and classify the singularities of characters through Harish-Chandra's differential equation. We have a program to develop these researches in future.

在过去的15年中，由于Fefferman-Stein，Carleson和其他人的结果，经典的谐波分析是过去15年的开花。我们计划的目的是研究经典谐波分析的概念，并在研究所与我们研究所的几位专家进行协调研究的各个领域中开发了它。我们的结果提取以下是：1。显示了在产品测量空间上运算符的插值定理。作为应用程序，我们在Riesz-Bochner手段和Kakeya的最大功能上部分解决了问题。研究了产品空间上的强大空间，并与两个变量的全态函数有关。我们现在正在将经典的耐力空间理论概括为负曲率的多种。2。我们已经研究了非线性演化方程在t = 0附近的Navier-Stokes方程溶液的属性，全局溶液的存在和解决方案的分类中获得了多个结果。3。通过一种D模型的方法，它可以通过Harish-Chandra的微分方程来成功地分析和分类角色的奇点。我们有一个计划来发展这些研究。

项目成果

HOTTA,Ryoshi: "Introduction to D-Modules" Institute of Mathematical Sciences,Madras, (1986)

HOTTA,Ryoshi：“D 模块简介”，马德拉斯数学科学研究所，（1986 年）

IGARI,Satoru: "Interpolation of linear operators in Lebesgue spaces with mixed norm and its applications to Fourier analysis" Tohoku Mathematical Journal. 38. 469-490 (1986)

IGARI，Satoru：“具有混合范数的勒贝格空间中线性算子的插值及其在傅里叶分析中的应用”东北数学杂志。

IGARI Satoru: Tohoku Math.J.38. 469-490 (1986)

IGARI 悟：东北数学.J.38。

HOTTA, Ryoshi: Institute of Mathematical Sciences, Madras. Introduction to D-Modules, (1986)

HOTTA, Ryoshi：数学科学研究所，马德拉斯。

HOTTA, Ryoshi: "Local formula for Springer's representation" Advanced Studies in Pure Mathematics. 6. 127-138 (1985)

HOTTA，Ryoshi：“施普林格表示的局部公式”纯数学高级研究。