1989 Fiscal Year Final Research Report Summary
Theory of analytic functions and its applications.
| Project/Area Number |
63540117
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
TAKEUTI Akira Kyoto University Yoshida College Professor, 教養部, 教授 (40026761)
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| Co-Investigator(Kenkyū-buntansha) |
KONO Norio Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (90028134)
NISIWADA Kimimasa Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (60093291)
MORIMOTO Yosinori Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (30115646)
UEDA Tetuo Kyoto University Yoshida College Professor, 教養部, 助教授 (10127053)
ASANO Kiyoshi Kyoto University Yoshida College Professor Assistant, 教養部, 教授 (90026774)
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| Project Period (FY) |
1988 – 1989
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| Keywords | Local Analytic Transformation / Pseudoconcave Set Of General Order / Singularities of Analytic Sets / Non-linear Cauchy-Kowalevski Theorem / SOS model / Self-similar Function / Estimate of Distribution Tail |
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| Research Abstract |
In our research we pursued the study of the theory of analytic functions and related topics. Below we state the summary of results obtained. I. In the study of the local structure of an analytic transformation of two complex variables,it was a difficult problem to obtain the canonical form of the transformation when one of the eigenvalue of the linear part is equal to I. In this case we succeeded in elucidate the complicated local structure. 2.A property of pseudconvex sets of lower order is found and some new properties of essential singularities if analytic sets are acquainted. 3. A new proof is given to Cox's theorem on the hilomorphic structure of the arithmetic-geometric mean of Gauss. 4. A simplified proof of non-linear Cauchy-Kowalevski theorem,which is fundamental in the theory of PDE,is obtained This proof is based only on the contraction mapping principle. 5.An estimate for degenerate Schrodinger operators is obtained,and applying it some results concerning infinitely degenerate elliptic operators are acquired 6. Star-triangular relations and combinatorial equalities are shown for solid-on-solid(SOS) models in statistical mechanics and their connections with modular functions are clarified. 7.A necessary and sufficient condition for a self-similar function to be absolutely continuous is given. 8. In the study of Gaussian process with non-constant variance,a sharp estimate for the distribution tails is obtained.As for the study of analytic differential systems with singularities,though it was developed considerably,more effort must be continued to integrate the research into publishable form. As stated above,our research established many excellent results in various topics and now still continued,and therefore,further development can be expected.
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