Research of Analysis on Clifford Algebra and it's Application
Project/Area Number  09640201 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
解析学

Research Institution  Fukuoka University of Education 
Principal Investigator 
NONO Kiyoharu Fukuoka University of Education, Education, Professor, 教育学部, 教授 (10117046)

CoInvestigator(Kenkyūbuntansha) 
HARA Takuya Fukuoka University of Education, Education, Associate Professor, 教育学部, 助教授 (50263984)
SAKAMOTO Takanori Fukuoka University of Education, Education, Associate Professor, 教育学部, 助教授 (00162313)
TAMARI Fumikazu Fukuoka University of Education, Education, Professor, 教育学部, 教授 (70036937)
FUKUTAKE Takayoshi Fukuoka University of Education, Education, Professor, 教育学部, 教授 (60036887)

Project Period (FY) 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,300,000 (Direct Cost : ¥2,300,000)
Fiscal Year 1998 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1997 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  Clifford Function Theory / Clifford Analysis / Clifford Algebra / EulerPoissonDarboux Equation / Generalized CauchyRiemann Equation / Generalized CauchyRiemann方程式 / EulerPoissonDarbour方程式 
Research Abstract 
The purpose of this research is "Composition of theory of functions based on important second order partial differential equation which appears in the mathematical physics". In this research, we focused on the following Generalized EulerPoissonDarboux's equations : SIGMA<@D3s(/)i=1@>D3<@D7*<@D12@>D1u(/)*x<@D12@>D1<@D2i@>D2@>D7  SIGMA<@D3n(/)i=s+1@>D3<@D7*<@D12@>D1u(/)*x<@D12@>D1<@D2I@>D2@>D7 *<@D7n1(/)x<@D2k@>D2@>D7 <@D7*u(/)*x<@D2k@>D2@>D7=O (O<less than or equal>s<less than or equal>n, l<less than or equal and constituted a function theory based on the equations. At first, we studied on the linearizations of the above second order partial differential equations. Using this linearizations(Generalized CauchyRiemann equations), we defined a regularity of functions with vales in Clifford algebra and obtained various properties of regular functions. Also, the compornent functions of a Clifford valued regular function are all solutions of the generalized EulerPoissonDarboux's equation. Reversely, we obtained the method to construct regular function from any solutions of the generalized EulerPoissonDarboux's equation. Therefore, we could perfectly construct the function theory based on Generalized EulerPoissonDarboux's equations. The results obtained in this research include the function theories based on Laplace equation and Generalized axially symmetric potential theory equations. Also, this function theory can be expected to develop in the future. The investigators, Fukutake and Hara obtained the several results on the topology and the operator theory, respectively.

Report
(3results)
Research Output
(9results)