Analytic functionals on the complex sphere

复球面上的解析泛函

基本信息

批准号：
11640181
负责人：
MORIMOTO Mitsuo
金额：
$ 1.73万
依托单位：
International Christian University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640181/
关键词：
Complex sphere Analytic functional Harmonic function Entire function of exponential type Fourier-Borel transformation Reproducing kernel Lie ball Dual Lie ball フーリェ・ボレル変換

项目摘要

In connection with that analytic functions and analytic functionals on the compex sphere are as boundary values of holomorphic harmonic functions in the Lie ball, we treat in [1] an integral rep-resention of Cauchy-Hua type. The entire functions which are the Fourier-Borel image of analytic functionals on the complex sphere are eigenfunctions of the Laplacian operator. In [2] we represent these eigenfunctions as an integral over the complex light cone. In [3] we treat the Fourier transfor-mation on the Hardy space of harmonic functions on the Lie ballIn [5] we study the reproducing kernel related with the complex sphere. In the papers [6] and [7] we discuss the relation between generalized functions, e.g., distributions, hyperfunctions, on the (real) sphere and solutions of the heat conduction equation. In [6] we study the one dimensional case, while in [7] we consider the n-dimensional sphere. These studies rely on the head investigator's results on the sphererical harmonic expansion of generalized functions on the real sphere. In [8] we study the double series expansion of holomorphic functions on the Lie ball, the dual Lie ball, or the complex Euclidean ball. [12] is a survey paper on the double series expansion. The last paper [13] shows there are a series of norms on the complex Euclidean space including the Lie norm, the dual Lie norm and the Euclidean norm. The result is given with calculationIn [11] we study how to define the Boehrnians on the sphere. The Boehmian is a generalized function usually defined on the Euclidean space by means of convolution. The convolution on the Euclidean space is a commutative operation but the convolution on the rotation group is not. We show two methods to overcome this difficulty

与Compex球上的分析函数和分析功能有关，是Lie Ball中抛态谐波函数的边界值，我们在[1]中对待Cauchy-Hua类型的整体rep-延长。整个功能是复杂球上分析功能的傅立叶图像，是拉普拉斯运算符的本征函数。在[2]中，我们表示这些本征函数是复杂的光锥上不可或缺的积分。在[3]中，我们在Lie Ballin上的谐波函数的强大空间上处理傅立叶trans transfor-Mation [5]，我们研究了与复杂球相关的繁殖核。在论文[6]和[7]中，我们讨论了广义函数，例如（真实的）球体和热传导方程的解决方案之间的分布，超功能。在[6]中，我们研究了一维情况，而在[7]中，我们考虑了N维球体。这些研究依赖于负责人研究者的结果，这些结果是在实际领域广义函数的球形谐波扩展。在[8]中，我们研究了在Lie Ball，Dual Lie Ball或Complecter Euclidean Ball上全体形函数的双重系列扩展。 [12]是有关双系列扩展的调查文件。最后一篇论文[13]表明，复杂的欧几里得空间有一系列规范，包括谎言规范，双重谎言规范和欧几里得规范。通过计算[11]给出了结果，我们研究了如何在球体上定义Boehrnians。 Boehmian是通常通过卷积在欧几里得空间上定义的广义函数。欧几里得空间上的卷积是一个交换的操作，但旋转组的卷积不是。我们展示了克服这个困难的两种方法