1987 Fiscal Year Final Research Report Summary
Bergman kernel function and canonical domains
| Project/Area Number |
61540098
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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 | Nagoya Institute of Technology |
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Principal Investigator |
MATSUURA Shozo Nagoya Institute of Technology, Professor, 工学部, 教授 (20024151)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAMOTO Kazuhiro Nagoya Institute of Technology, Assistant Professor, 工学部, 助教授 (30091515)
KURATA Masahiro Nagoya Institute of Technology, Assistant professor, 工学部, 助教授 (10002164)
TODA Nobushige Nagoya Institute of Technology, Professor, 工学部, 教授 (30004295)
NAKAI Mitsuru Nagoya Institute of Technology, Professor, 工学部, 教授 (10022550)
HAYASHI Eiichi Nagoya Institute of Technology, Professor, 工学部, 教授 (80024173)
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| Project Period (FY) |
1986 – 1987
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| Keywords | Analytic mapping / Bergman kernel / Szego kernel / HL_2-minimum problem / Canonical domain / Circular domain / シュワルツ定数 |
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| Research Abstract |
The main objects of this research are to study the reproducing kernels, properties of many types of canonical dimains and their applications to various extremal problems. First we construct the Szego kernel on a bounded complete circular domain using of an orthonormal system on its Silov boundary and give the solutions of L_2-minimum problems on the Silov boundary in terms of the Szego kernel. As its application we get a reasonable generalization of Y. Kubota's extremal theorem which is a higher dimensional generalization of the Riemann mapping theorem for bounded symmetric domains.
Next, using properties of canonical domains and a generalized Schwarz-Pick type lemma between arbitrary two bounded homogeneous domains obtained in our research, we give the generalized Schwarz constant (the best possible constant in the lemma) between two arbitrary classical Cartan domains. We can show that in the case of Cartan domains each Ahlfors type coefficient of the Schwarz lemma (for Kahler manifolds) given by Yau coincides with our Schwarz constant and so is best possible. Incidentally we slightly ammend thw Schwarz constants of product Cartan domains given by K. H. Look.
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