On analytic functionals on the complex sphere

论复球面上的解析泛函

• 批准号: 14540184
• 负责人: MORIMOTO Mitsuo
• 金额: $ 2.24万
• 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: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540184/
• 关键词: analytic functional; Lie ball; complex sphere; Boehmian; Enri Kohai jutsu; the "Tetsujutsu Sankei"; Japanese traditional mathematics; Takebe Katahiro; 算学啓蒙; 天元術; Boehmian

1) Characterization of generalized functions as initial values of solutions of the heat equation.2) Relationship of two definitions of Boehmians on the sphere.3) Jointly with Keiko Fujita, we could present explicitly the Bergman kernel for the Np ball, which is a generalization of the Lie ball and the dual Lie ball. Concerning this, Jong-Do Kim (Seoul) gave a more explicit formula for the N4 ball. We examine his result.4) I organized the 12^<th> International Conference on Finite or Infinite Dimensional Complex Analysis and Applications at International Christian University on July 27-31, 2004. Among about 100 foreign participants is Professor Sheng Gong, Chinese specialist on Complex Analysis. The proceedings was published from Kyushu University Press in May, 2005 with 46 papers presented at the conference.5) Jointly with Tsukane Ogawa, I published an article entitled "Mathematics of Takebe Katahiro" in the journal "Sugaku" (Mathematics) of the Mathematical Society of Japan. We review … More ed the life of Takebe, who was a high ranked government officer of the early 18th century, and discussed his three formulas of the inverse sine function, one of which was the Taylor expansion formula.6) The above mentioned Taylor expansion formula was obtained in the "Tetsujutsu Sankei" by a numerical-analytic method. Later, Takebe proved the same formula by a completely different algebraic method. Takebe and Seki learned the Chinese mathematics, among others, the method of root extraction and the method of celestial element. They constructed the so-called "counting board algebra" which is isomorphic to the polynomial algebra of modern mathematics. The algebraic method to obtain the Taylor expansion formula was also derived from these two methods of Chinese traditional mathematics.7) Jointly with Tsukane Ogawa, I am translating the "Tetsujutsu Sankei" into English. The first draft was checked by Dr. Paul Ishiwara. We are now preparing mathematical commentaries.8) Several unpublished papers on Japanese traditional mathematics were published on the web (Science Research Report, International Christian University) http://science.icu.ac.jp/srr/ Less

1) 将广义函数表征为热方程解的初始值。2) 球面上 Boehmians 的两个定义的关系。3) 与 Keiko Fujita 一起，我们可以明确地提出 Np 球的伯格曼核，其中是李球和双李球的概括，Jong-Do Kim（首尔）给出了 N4 球的更明确的公式。4）我组织了第12届有限或无限维复分析及应用国际会议，2004年7月27日至31日在国际基督教大学举行。大约100名外国与会者中有中国复分析专家宫盛教授。论文集由九州出版。 2005年5月大学出版社在会议上发表了46篇论文。5）与Tsukane Okawa联合发表了一篇题为“Mathematics of Takebe”的文章Katahiro”发表在日本数学会的期刊《Sugaku》（数学）中。我们回顾了 18 世纪初一位高级政府官员武部的一生，并讨论了他的三个反正弦公式函数，其中之一就是泰勒展开式。6）上述泰勒展开式是在《铁术产经》中用数值解析的方法得到的。后来，武部用完整的方法证明了同样的公式。武部和关学习了中国数学的求根法、天元法等，他们构造了与现代数学的多项式代数同构的所谓“算板代数”。获得泰勒展开式的方法也是从中国传统数学的这两种方法推导出来的。7）我与小川冢音一起将《铁术产经》翻译成英文。初稿由 Paul Ishiwara 博士检查。我们现在正在准备数学评论。8) 几篇关于日本传统数学的未发表论文发表在网络上（科学研究报告，国际基督教大学）http://science.icu。 .ac.jp/srr/ 更少

项目成果

Generalized functions on the sphere and heat functions

球面上的广义函数和热函数

• 发表时间: 2002
• 期刊: Proc. of the third Asian Mathematical Conf.2000(World Scientific)
• 作者: 森本光生;小川束;M.Morimoto;M.Morimoto;M.Morimoto;M.Morimoto;M.Morimoto
• 通讯作者: M.Morimoto

森本光生: "逆三角関数に関する建部賢弘の三つの公式"Science Research Report, International Christian U. GS-0304(on the web). (2003)

Mitsuo Morimoto：“Tatehiro Takebe 的三个反三角函数公式”科学研究报告，国际基督教 U. GS-0304（网络）（2003 年）。

K.S.Wang, H.Suzuki: "Weakly Distance-Regular Digraphs"Disuete Math.. 264. 225-236 (2003)

K.S.Wang，H.Suzuki：“弱距离-正则有向图”Disuete Math.. 264. 225-236 (2003)

M.MORIMOTO: "Boehmians on the sphere and zonal spherical function"Microlocal Analysis and Complex Fourier Analysis World Scientific. 224-237 (2002)

M.MORIMOTO：“关于球面和带状球面函数的波姆主义者”微局域分析和复杂傅立叶分析世界科学。

森本光生: "Analytic functions and analytic functionals on some balls in the complex Euclidean space"Analysis and Applications - ISAAC2001, Kluwer Academic Publishers Netherlands. 151-159 (2003)

Mitsuo Morimoto：“复杂欧几里德空间中某些球上的解析函数和解析泛函”分析和应用 - ISAAC2001，荷兰 Kluwer 学术出版社 151-159 (2003)。