1998 Fiscal Year Final Research Report Summary
CONSTRUCTION OF ANALYSIS ON COMPLEX MANIFOLD
| Project/Area Number |
08454035
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | SOPHIA UNIVERSITY |
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Principal Investigator |
YOSINO Kunio Sophia Univ.Math.Lecturer, 理工学部, 講師 (60138378)
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| Co-Investigator(Kenkyū-buntansha) |
MORIMOTO Mitsuo International Catholic Univ.Math.Professor, 教授 (80053677)
KANEYUKI Souji Sophia Univ.Math.Professor, 理工学部, 教授 (40022553)
TAHARA Hidetoshi Sophia Univ.Math.Professor, 理工学部, 教授 (60101028)
OUCHI Sunao Sophia Univ.Math.Professor, 理工学部, 教授 (00087082)
UCHIYAMA Kouichi Sophia Univ.Math.Professor, 理工学部, 教授 (20053689)
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| Project Period (FY) |
1996 – 1998
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| Keywords | Complex Manifold / Analytic Functional / Partial Differential Equation / Singularity / asymptotic Expansion / Computer / Integer theory / Algebra |
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| Research Abstract |
1. (1)The meaning of Ramanujan's integral formula and Rananujan' summation formula are given by using the theory of analytic functionajs. Especially, relation between Ramauujan's integral formula and sampling theorem is clarified. (2)The structure of analytic functionaiB on real sphere, complex sphere and Lie sphere are studied.
2. (1)Uniqueness of solution to Fuchujan partial differential equations, (2)Gevrey asymptotic behavior of formal solutions of partial differential equations (3) Behavior of Davey-Stewartson are considered.
3. Conformal group, orbit decomposition in symmetric spaces are determined. Reconstruction of graded Lie algebra are done.
4. Zeta function associated to Riemaniann symmetric spaces and Shintani function are determined.
5. Computer method to visualize the stokes line (which is important in complex WKB analysis) is developped.
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