1990 Fiscal Year Annual Research Report

大域解析学における諸問題の研究

Research Project

Project/Area Number	02452004
Research Institution	Keio University
Principal Investigator	小畠守生慶應義塾大学, 理工学部, 教授 (90087015)
Co-Investigator(Kenkyū-buntansha)	前田吉昭慶應大学, 理工学部, 助教授 (40101076) 前島信慶應大学, 理工学部, 教授 (90051846) 伊藤雄二慶應大学, 理工学部, 教授 (90112987) 田中洋慶應大学, 理工学部, 教授 (70011468) 菊池紀夫慶應大学, 理工学部, 教授 (80090041)
Keywords	ヤングミルズ場 / 調和写像 / 変分問題の安定性 / 作用素環 / セルフシミラリティ- / フラクタル / 結び目理論 / マルコフ過程
Research Abstract	今年度は主として多様体上における解析,特に非線型偏微分方程式の幾何学的取り扱い,多様体上の確率過程,等に重点をおいた研究が行なわれた。菊池,谷による変分問題の解の存在及び正則性について,微分方程式の立場と変分法の立場から同時に解析がされ,調和写像や一般流体の方程式に対する自由境界値問題について結果が出された。前田をはじめとし,ヤングミルズ場の安定性についても上記の解析に深く関連し弱解の存在をはじめ正則性に関するいくつかの結果が得られつつある。一方,前田他により,非可換多様体の構成問題が行なわれた。これは,微分作素環を基にして,従来の多様体上に代数束を構成するものであり,この1つの応用として,変形量子化の一般的可能性について結果を示すことが出来た。現在これらの応用として,ワイル多様体の幾何学的構造の解明,又,偏微分方程式論への関連について研究が進められている。伊藤,仲田,金井他による負曲率多様体上のエルゴ-ド理論の研究について,著しい進展が得られた。特に仲田によるディオファンタス近似の計量的性質と3次元上手平面の無限遠点での大域的性質との関係が指摘された。自己相似性に関して,前島他らによる研究も多くなされ,自己相似的安定性,定常増分をもつ自己相似安定性についての例や既知の結果の総括,又確率過程の無限級数展開について新しい結果を生んでいる。その他,田中によるランダムウォ-クの時間反転,黒田他による,ギブス点過程についての中心極限定理,小山によるル-プ群についてのセ-タ関数の性質,塩川他による数論の幾何学的立場からの説明,又,有限幾何や,離散幾何学の応用として組合せ理論やグラフ理論への問題について榎本他の多くの研究がなされている。

Research Products
(23 results)

All Other

All Publications (23 results)

[Publications] N.Kikuchi: "Companato type estimates for solutions of differenceーelliptic partial differential equations with constant coefficients" Rendiconti Del Circolo Mathematico Di Palermo. 30. 99-131 (1990)
[Publications] S.Koyama: "Determinant expression of Selberg zeta functions,I,II,III" Transactions of American Mathematical Society.
[Publications] H.Naito,H.Kozono,Y.Maeda: "A stable manifold theorem for the YangーMills gradient flow" Tohoku Mathematical Journal. 42. 45-66 (1989)
[Publications] H.Tanaka: "Time reversal of random walks in R^d" Tokyo Journal of Mathematics. 13. 375-389 (1990)
[Publications] H.Nakada: "The metrical theory of complex continued fractions" Acta Arith.56ー3.
[Publications] H.Kozono,Y.Maeda: "On asymptotic stability for the YangーMills gradient flow" Tokyo Journal of Mathematics. 12. 387-414 (1989)
[Publications] H.Omori,Y.Maeda,A.Yoshioka: "Weyl manifolds and deformation quantization" Adv.Math.
[Publications] H.Omori,Y.Maeda,A.Yoshioka: "Global calculas on Weyl manifolds" Japanese J.Math.
[Publications] H.Omori,Y.Maeda,A.Yoshioka: "nonーcommutative complex projective spaces" Adv.Stud.Pure.Math.
[Publications] I.Shiokawa,J.Tamura: "Pade Approximations to certain power series"
[Publications] Y.Nakai,I.Shiokawa: "A class of normal numbers"
[Publications] K.kuroda,H.Tanemura: "Limit theorem and large deviation principle for Voronoi tessellation generated by Gibbs point process"
[Publications] S.Koyama: "zeta functions of Loop groups" Adv.Stud.Pure Math.
[Publications] H.Nakada,G.Wagner: "DuffinーSchaeffer theorem of Diophantine Approximation for complex numbers" Journ.Arith.
[Publications] H.Enomoto,H.Mizutani N.Tokushige: "A word problem in Coxeter semigroup" Discrete Math.
[Publications] H.Enomoto M.kano: "Disjoint odd interger.subsets having a constant even sum"
[Publications] H.Enomoto: "Minimum number of edges in 2ーconnected graphs"
[Publications] H.Enomoto: "Graph decompositions without isolated vertices"
[Publications] V.A.Solonnkov,A.Tani: "Free boundary problem for a viscous compressible flow with a surface tension" C.Caratheodory International Tributes.
[Publications] N.Kono,M.Maejima: "Selfーsimilar stable processes with stationary increments" Proc.for the Workshop on stable processes and Related Topics.
[Publications] N.Kono,M.Maejima: "Holder continuity of some self similar stable processes" Tokyo J.Math.
[Publications] S.cambanis,Y.Maejima,G.Samorodnitsky: "Characterizations of the linear and harmonizable fractional stable motions"
[Publications] M.Maejima,Y.Morita: "Trimmed sums of mixing triangular arrays with stationary rows"

1990 Fiscal Year Annual Research Report

大域解析学における諸問題の研究

Principal Investigator

小畠 守生 慶應義塾大学, 理工学部, 教授 (90087015)

Research Products

[Publications] N.Kikuchi: "Companato type estimates for solutions of differenceーelliptic partial differential equations with constant coefficients" Rendiconti Del Circolo Mathematico Di Palermo. 30. 99-131 (1990)

[Publications] S.Koyama: "Determinant expression of Selberg zeta functions,I,II,III" Transactions of American Mathematical Society.

[Publications] H.Naito,H.Kozono,Y.Maeda: "A stable manifold theorem for the YangーMills gradient flow" Tohoku Mathematical Journal. 42. 45-66 (1989)

[Publications] H.Tanaka: "Time reversal of random walks in R^d" Tokyo Journal of Mathematics. 13. 375-389 (1990)

[Publications] H.Nakada: "The metrical theory of complex continued fractions" Acta Arith.56ー3.

[Publications] H.Kozono,Y.Maeda: "On asymptotic stability for the YangーMills gradient flow" Tokyo Journal of Mathematics. 12. 387-414 (1989)

[Publications] H.Omori,Y.Maeda,A.Yoshioka: "Weyl manifolds and deformation quantization" Adv.Math.

[Publications] H.Omori,Y.Maeda,A.Yoshioka: "Global calculas on Weyl manifolds" Japanese J.Math.

[Publications] H.Omori,Y.Maeda,A.Yoshioka: "nonーcommutative complex projective spaces" Adv.Stud.Pure.Math.

[Publications] I.Shiokawa,J.Tamura: "Pade Approximations to certain power series"

[Publications] Y.Nakai,I.Shiokawa: "A class of normal numbers"

[Publications] K.kuroda,H.Tanemura: "Limit theorem and large deviation principle for Voronoi tessellation generated by Gibbs point process"

[Publications] S.Koyama: "zeta functions of Loop groups" Adv.Stud.Pure Math.

[Publications] H.Nakada,G.Wagner: "DuffinーSchaeffer theorem of Diophantine Approximation for complex numbers" Journ.Arith.

[Publications] H.Enomoto,H.Mizutani N.Tokushige: "A word problem in Coxeter semigroup" Discrete Math.

[Publications] H.Enomoto M.kano: "Disjoint odd interger.subsets having a constant even sum"

[Publications] H.Enomoto: "Minimum number of edges in 2ーconnected graphs"

[Publications] H.Enomoto: "Graph decompositions without isolated vertices"

[Publications] V.A.Solonnkov,A.Tani: "Free boundary problem for a viscous compressible flow with a surface tension" C.Caratheodory International Tributes.

[Publications] N.Kono,M.Maejima: "Selfーsimilar stable processes with stationary increments" Proc.for the Workshop on stable processes and Related Topics.

[Publications] N.Kono,M.Maejima: "Holder continuity of some self similar stable processes" Tokyo J.Math.

[Publications] S.cambanis,Y.Maejima,G.Samorodnitsky: "Characterizations of the linear and harmonizable fractional stable motions"

[Publications] M.Maejima,Y.Morita: "Trimmed sums of mixing triangular arrays with stationary rows"

小畠守生慶應義塾大学, 理工学部, 教授 (90087015)