1990 Fiscal Year Annual Research Report

大域解析における諸問題

Research Project

Project/Area Number	01460003
Research Institution	Tohoku University
Principal Investigator	小竹武東北大学, 理学部, 教授 (30004427)
Co-Investigator(Kenkyū-buntansha)	新井仁之東北大学, 理学部, 講師 (10175953) 板東重稔東北大学, 理学部, 助教授 (40165064) 伊藤秀一東北大学, 理学部, 助教授 (90159905) 高木泉東北大学, 理学部, 助教授 (40154744) 加藤順二東北大学, 理学部, 教授 (80004290)
Keywords	シュレディンガ-方程式 / ハミルトン力学系 / 関数微分方程式 / 調和関数 / バ-グマン核
Research Abstract	1.偏微分方程式論およびその幾何学への応用に関するものとして、正のポテンシャルをもつシュレディンガ-方程式に対する固有値の漸近分布についての研究、リ-マン多様体上の熱方程式に対する解の一意性定理の証明、正則ベクトル束の特異点除去可能性とリッチ曲率との関連についての研究等が挙げられる。 2.力学系理論の分野では、解析的かつ可積分なハミルトン力学系について、特異点近傍での正規型への還元問題や解の解析接続とホロノミ-群との関係について新しい結果が得られた。また、無限の遅れをもつ関数微分方程式に関して、解の大域的存在、有界性、安定性等について種々の十分条件が示された。 3.非線型解析での成果としては、拡散・交応方程式系に対する大域解の定性的、定量的研究、特に、解の幾何学的研究として、パタ-ン形成と特異点発生について興味ある結果が得られた。 4.調和解析の分野では、強擬凸領域上のラプラス作用素に関する調和測度の正則性についての研究、調和関数の境界挙動についての研究等が挙げられる。一方、作用素論においても、作用素環の順序構造と正則完備化の構造との関係について新しい知見が得られた。 5.強擬凸領域上のバ-グマン核の研究として、領域が特に二次元ラインハルト領域のとき、バ-グマン核のトレ-スの境界近傍での漸近展開と境界のチャ-ン・モ-ザ-不変多項式との関係が明確化され、この結果、二次元複素球の大域的特徴づけが得られた。

Research Products

(17 results)

All Other

All Publications (17 results)

[Publications] 新井仁之: "Estimates of harmonic measures associated with degenerate Laplacian on strictly pseudoconvex domains" Proc.Japan Acad.66. 13-15 (1990)
[Publications] 伊藤秀一: "On the holonomy group associated with analytic continuations of solutions for integrable systems" Bol.Soc.Bras.Mat. 21. 95-120 (1990)
[Publications] 加藤順二: "Compact boundedness in periodic functional differential equations with infinite delay" Proc.Royal Soc.Edinburgh. 114. 291-297 (1990)
[Publications] 斎藤和之: "Embeddable AW^*ーalgebras and regular completions" J.London Math.Soc.34. 511-523 (1990)
[Publications] 立沢一哉: "Asymptotic distribution of eigenvalues of Schro^^¨dinger operators with nonーClassical potentials" Tohoku Math.J.42. 381-406 (1990)
[Publications] 高木泉 (第一著者,W.N.Ni): "On the shape of leastーenergy solutions to a semilinear Neumann problem" Comm.Pure and Applied Math.
[Publications] 今野一宏: "Generic Torelli theorem for hypersurfaces of certain compact homogeneous Ka^^¨hler manifolds" Duke Math.J.59. 83-160 (1989)
[Publications] 斎藤和之: "Embeddable AW^*ーalgebras and regular eompletions" J.London Math.Soc.34. 511-523 (1990)
[Publications] 立沢一哉: "Asymptotic distribution of eigenvalues of Schro^^¨dinger oprators with non classical potentials" Tohoku Math.J.42. 381-406 (1990)
[Publications] 立沢一哉: "Eigenvalue asymptotics of Schro^^¨dinger oprators with positive potentials" Tohoku Math.J.
[Publications] 高木泉 (第一著者,W.N.Ni): "On the shape of least energy solutions to a semilinear Neumann problem" Comm.Pure and Applied Math.
[Publications] 長澤壮之: "Asymptotical stability of YangーMills' gradient flow" “Geometry of Manifolds." Academic press. 499-517 (1989)
[Publications] 長澤壮之: "Uniqueness and Widder's theorems for the heat equation on Riemannian manifolds" preprint.
[Publications] 中澤則之: "Asymptotic Expansion of the Bergman Kernel for Steictly Pseudoconvex Complete Reinhardt Domains in C^2" Proc.Japan Acad.66. 39-41 (1990)
[Publications] 板東重稔: "Bubbling out of Einstein manifolds" Tohoku Math.J.42. 175-180 (1990)
[Publications] 板東重稔: "Removable singularities for holomorphic vector bundles" Tohoku Math.J.
[Publications] 堀畑和弘: "Pointwise property of L^pーfunctions with Nikolskii condition" Bolletino della Unione Matematica I taliana. 7. 199-207 (1989)

1990 Fiscal Year Annual Research Report

大域解析における諸問題

Principal Investigator

小竹 武 東北大学, 理学部, 教授 (30004427)

Research Products

[Publications] 新井 仁之: "Estimates of harmonic measures associated with degenerate Laplacian on strictly pseudoconvex domains" Proc.Japan Acad.66. 13-15 (1990)

[Publications] 伊藤 秀一: "On the holonomy group associated with analytic continuations of solutions for integrable systems" Bol.Soc.Bras.Mat. 21. 95-120 (1990)

[Publications] 加藤 順二: "Compact boundedness in periodic functional differential equations with infinite delay" Proc.Royal Soc.Edinburgh. 114. 291-297 (1990)

[Publications] 斎藤 和之: "Embeddable AW^*ーalgebras and regular completions" J.London Math.Soc.34. 511-523 (1990)

[Publications] 立沢 一哉: "Asymptotic distribution of eigenvalues of Schro^^¨dinger operators with nonーClassical potentials" Tohoku Math.J.42. 381-406 (1990)

[Publications] 高木 泉 (第一著者,W.N.Ni): "On the shape of leastーenergy solutions to a semilinear Neumann problem" Comm.Pure and Applied Math.

[Publications] 今野 一宏: "Generic Torelli theorem for hypersurfaces of certain compact homogeneous Ka^^¨hler manifolds" Duke Math.J.59. 83-160 (1989)

[Publications] 斎藤 和之: "Embeddable AW^*ーalgebras and regular eompletions" J.London Math.Soc.34. 511-523 (1990)

[Publications] 立沢 一哉: "Asymptotic distribution of eigenvalues of Schro^^¨dinger oprators with non classical potentials" Tohoku Math.J.42. 381-406 (1990)

[Publications] 立沢 一哉: "Eigenvalue asymptotics of Schro^^¨dinger oprators with positive potentials" Tohoku Math.J.

[Publications] 高木 泉 (第一著者,W.N.Ni): "On the shape of least energy solutions to a semilinear Neumann problem" Comm.Pure and Applied Math.

[Publications] 長澤 壮之: "Asymptotical stability of YangーMills' gradient flow" “Geometry of Manifolds." Academic press. 499-517 (1989)

[Publications] 長澤 壮之: "Uniqueness and Widder's theorems for the heat equation on Riemannian manifolds" preprint.

[Publications] 中澤 則之: "Asymptotic Expansion of the Bergman Kernel for Steictly Pseudoconvex Complete Reinhardt Domains in C^2" Proc.Japan Acad.66. 39-41 (1990)

[Publications] 板東 重稔: "Bubbling out of Einstein manifolds" Tohoku Math.J.42. 175-180 (1990)

[Publications] 板東 重稔: "Removable singularities for holomorphic vector bundles" Tohoku Math.J.

[Publications] 堀畑 和弘: "Pointwise property of L^pーfunctions with Nikolskii condition" Bolletino della Unione Matematica I taliana. 7. 199-207 (1989)

小竹武東北大学, 理学部, 教授 (30004427)

[Publications] 新井仁之: "Estimates of harmonic measures associated with degenerate Laplacian on strictly pseudoconvex domains" Proc.Japan Acad.66. 13-15 (1990)

[Publications] 伊藤秀一: "On the holonomy group associated with analytic continuations of solutions for integrable systems" Bol.Soc.Bras.Mat. 21. 95-120 (1990)

[Publications] 加藤順二: "Compact boundedness in periodic functional differential equations with infinite delay" Proc.Royal Soc.Edinburgh. 114. 291-297 (1990)

[Publications] 斎藤和之: "Embeddable AW^*ーalgebras and regular completions" J.London Math.Soc.34. 511-523 (1990)

[Publications] 立沢一哉: "Asymptotic distribution of eigenvalues of Schro^^¨dinger operators with nonーClassical potentials" Tohoku Math.J.42. 381-406 (1990)

[Publications] 高木泉 (第一著者,W.N.Ni): "On the shape of leastーenergy solutions to a semilinear Neumann problem" Comm.Pure and Applied Math.

[Publications] 今野一宏: "Generic Torelli theorem for hypersurfaces of certain compact homogeneous Ka^^¨hler manifolds" Duke Math.J.59. 83-160 (1989)

[Publications] 斎藤和之: "Embeddable AW^*ーalgebras and regular eompletions" J.London Math.Soc.34. 511-523 (1990)

[Publications] 立沢一哉: "Asymptotic distribution of eigenvalues of Schro^^¨dinger oprators with non classical potentials" Tohoku Math.J.42. 381-406 (1990)

[Publications] 立沢一哉: "Eigenvalue asymptotics of Schro^^¨dinger oprators with positive potentials" Tohoku Math.J.

[Publications] 高木泉 (第一著者,W.N.Ni): "On the shape of least energy solutions to a semilinear Neumann problem" Comm.Pure and Applied Math.

[Publications] 長澤壮之: "Asymptotical stability of YangーMills' gradient flow" “Geometry of Manifolds." Academic press. 499-517 (1989)

[Publications] 長澤壮之: "Uniqueness and Widder's theorems for the heat equation on Riemannian manifolds" preprint.

[Publications] 中澤則之: "Asymptotic Expansion of the Bergman Kernel for Steictly Pseudoconvex Complete Reinhardt Domains in C^2" Proc.Japan Acad.66. 39-41 (1990)

[Publications] 板東重稔: "Bubbling out of Einstein manifolds" Tohoku Math.J.42. 175-180 (1990)

[Publications] 板東重稔: "Removable singularities for holomorphic vector bundles" Tohoku Math.J.

[Publications] 堀畑和弘: "Pointwise property of L^pーfunctions with Nikolskii condition" Bolletino della Unione Matematica I taliana. 7. 199-207 (1989)