2005 Fiscal Year Final Research Report Summary
On analytic functionals on the complex sphere
| Project/Area Number |
14540184
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | International Christian University |
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Principal Investigator |
MORIMOTO Mitsuo International Christian University, CLA, Professor, 教養学部, 教授 (80053677)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Hiroshi International Christian University, CLA, Professor, 教養学部, 教授 (10135767)
SHIMIZU Yuji International Christian University, CLA, Associate Prof., 教養学部, 準教授 (80187468)
YAMAKAWA Aiko International Christian University, CLA, Assistant Prof., 教養学部, 助教授 (80112754)
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| Project Period (FY) |
2002 – 2005
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| Keywords | analytic functional / Lie ball / complex sphere / Boehmian / Enri Kohai jutsu / the "Tetsujutsu Sankei" / Japanese traditional mathematics / Takebe Katahiro |
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| Research Abstract |
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
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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
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Research Products
(14 results)
