1993 Fiscal Year Final Research Report Summary
Several Problems in Analysis
| Project/Area Number |
03452006
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | TOHOKU UNIVERSITY |
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Principal Investigator |
SHIMAKURA Norio Tohoku University, Professor, 理学部, 教授 (60025393)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Kazuyuki 東北大学, 理学部, 助教授 (60004397)
NISHIKAWA Seiki 東北大学, 理学部, 教授 (60004488)
IGARI Satoru 東北大学, 理学部, 教授 (50004289)
KATO Junji 東北大学, 理学部, 教授 (80004290)
TOTAKE Takeshi 東北大学, 理学部, 教授 (30004427)
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| Project Period (FY) |
1991 – 1993
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| Keywords | Lyapunov function / Operating functions / Regular completion / Least energy solutions / Non-resonance condition / Hypergeometric singularities / Wilson basis / Bloch functions |
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| Research Abstract |
We effectuated researches of several problems in analysis, not only those in its proper domains but also in branches related to geometry and algebra. Our research activities during these three years were very vigorous and fruitful.
The head investigator completed the English translation of his textbook on partial differential operators of elliptic type, investigated a free boundary problem and the Bessel operator in matrix spaces. Researches by investigators were the floowing : Stability of differential equations with finite or infinite delaly by the Liapunov method (J.Kato) ; Birkhoff normal form near equilibrium points and integrability of Haniltonian systems (H.Ito) ; Reaction - diffusion systems with small diffusion constants and semilinear elliptic equations derived from them (I.Takagi) ; Hausdorff dimension of singularities of solutions for nonlinear elliptic equations (K.Horihata) ; Asymptotic expansion near the boundary of Bergman curbels for strictly pseudoconvex Reinhardt doma
… More
in (N.Nakazawa) ; Hypergeometric singularities of solutions for characteristic Cauchy problems (S.Fujiie) ; Potential theory and harmonic analysis for elliptic operators in strictly pseudoconvex domains (H.Arai) ; Law of asymptotic distribution of eigenalues for Schrodinger operators with non-classical p0otentials based on uncertainty principle (K.Tachizawa) ; Spectral geometry for Riemannian foliation and harmonic maps between hyperbolic spaces (S.Nishikawa) ; Characterization of operating functions in Fourier analysis on non compact commutative groups (S.Igari) ; Structure of C^* - algebras and their regular completions(K.Saito) ; and Einstein - Hermitian metrics in Kahler manifolds(S.Bando).
Furthermore, researches by co-operators were the following : Spectral analysis of magnetic Schrodinger operators under group actions (T.Sunada) ; Hypergeometric functions of several variables from the viewpoint of algebraic anallysis (R.Hotta) ; Yang-Baxter equation (K.Hasegawa) ; Distribution of rational points of hyperelliptic surfaces (Y.Morita) ; and Toric varieties (T.Oda and M.Ishida). Less
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