2001 Fiscal Year Final Research Report Summary
Conformal invariants of Riemann surfaces and theta functions
| Project/Area Number |
12640156
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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 | TOKYO GAKUGEI UNIVERSITY |
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Principal Investigator |
YAMADA Akira Tokyo Gakuqei University, Education, Professor, 教育学部, 教授 (60126331)
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| Co-Investigator(Kenkyū-buntansha) |
MASUMOTO Makoto Yamaguchi University, Science, Assistant professor, 理学部, 助教授 (50173761)
MIZOGUCHI Noriko Tokyo Gakugei University, Education, Assistant Professor, 教育学部, 助教授 (00251570)
KUBOTA Yoshihisa Tokyo Gakugei University, Education, Professor, 教育学部, 教授 (30014715)
YANAGIHARA Hiroshi Yamaguchi Univ ersity, Engineer, Assistant professor, 工学部, 助教授 (30200538)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Riemann Surface / conformal invariant / thetafunction / Ahlfors function / de Branges / Bloch function / complementary space |
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| Research Abstract |
In this year the head investigator continued his study of de Branges' complementation space that is closely related to the notion of the sum of kernel fun cfons. Analyzing the proof by de Branges of the Caratheodory-Fejer extension problem on the unit disk, he showed that a lemma about the existence of the contraction concerning an isometry and coisometry is essential in the proof. Using this lemma he showed simple alternative proof of the commutant lilting theorem due to Nagy : Foias. Also, he showed that the necessary and sufficient condition for the existence of the extended interpolation problem due to Ms. Takahashi in Nara Women 's University is obtained from the lemma by using elementary linear algebra.
Kubota showed a theorem that extends to the case of Banach spaces of the result obtained by Rosay-Rudin about the stable domains of the holomorphic automorphisms with fixed points on finite dimensional c omplex spaces.
Mizoguchi studied the asymptotic behavior of zeros of solutions for parabolic equations on the real line, and she proved that the zeros remain finite for a fixed blowup time.
Masumoto gave a simple alternative proof of the result alrea dy obtained by him that extremal lengths of homology classes on closed Riemann surfaces of finite positive genus satisfy an algebraic equation.
Yanagihara studied the variability region of the values f(a) at a fixed point for normalized Bloch functions f(z) on the unit disk. He determined its shape when the derivative at the origin is sufficiently small.
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