1998 Fiscal Year Annual Research Report

汎関数解析

Research Project

Project/Area Number	09440068
Research Institution	Department of Mathematics, Faculty of Sciences, Gakushuin University
Principal Investigator	藤原大輔学習院大学, 理学部, 教授 (10011561)
Co-Investigator(Kenkyū-buntansha)	一瀬孝金沢大学, 大学院・自然科学研究科, 教授 (20024044) 川崎徹郎学習院大学, 理学部, 助教授 (90107061) 片瀬潔学習院大学, 理学部, 教授 (70080489) 水谷明学習院大学, 理学部, 教授 (80011716) 黒田成俊学習院大学, 理学部, 教授 (20011463)
Keywords	Feynman 経路積分 / path integral / WKB法 / sfationary phare methos / 量子力学 / 準古典近似 / Schrodinger方程式 / ハミルトニアン
Research Abstract	1. 研究上重要な成果であるKumanogo-Taniguchi型の定理の新証明は論文にまとめ、雑誌Funkcialaj Eqvaciojに発表し、出版された。また、これを使って、熊の郷直人氏は、本来のKumanogo-Taniguchiの定理を改良した。代表者がここで開発した方法と熊の郷直人氏の方法とを併せると、磁場が存在する場合のLagrange関数に対して、Kumanogo-Taniguchi型の定理の新証明を作る可能性が出てきたが、十分な検討時間が無く未だ解明されていない。また、従来の方法では取り扱い不可能な形の汎関数にたいしても単純なばあいは、Kumanogo-Taniguchi型の評価を証明することが出来る見通しがついた。 2. 研究代表者は、1997年4月ドイツ連邦共和国のOberwolfach数学研究所で行われた国際会議において、Feynman経路積分について1時間のサーベイトークを行った。 3. 分担者黒田は、局所的に非常に強い特異性をもつポテンシアルをもつハミルトンニアンが、本質的自己共役と成るための条件に関して新しい結果を得た。これは、一部分は、長谷氏との共同研究である。結果はチェコスロバキアの原子核研究所での研究集会で発表した。 4. 分担者水谷は、非線形の楕円型と放物型偏微分方程式の研究に有限要素法を適用して成果を上げ、これを発表した。 5. 分担者渡辺は、磁場のある場合のShrodinger方程式の散乱行列の位相の研究に研究成果をあげ、専門分野の雑誌に投稿し掲載された。 6. 分担者一瀬はTrotter-Kato型の定理の収束に関し、その収束のノルムの強さと収束の早さに付き新しい結果を得て発表し掲載された。

Research Products

(16 results)

All Other

All Publications (16 results)

[Publications] D.Fujiwara and T.Tsuchida,: "The time slicing approximation of the fundamental solution for the Schrodinger equation with electromagnetic fields" Journal of the Math.Soc.Japan.vol.49. 299-327 (1997)
[Publications] D.Fujiwara,N.Kumano-go,K.Taniguchi: "A proof of estimates of Kumano-go-Taniguchi type for multiproduct of Fourier integral operators" Funkcialaj Ekvacioj. vol.40. 459-470 (1997)
[Publications] T.Ichinose and S.Takanobu: "On the norm estimate of the difference between the Kac operator and the Schrodinger semigroup" Differential Equations,Asymptotic Analysis and Mathematical Physics. vol.100. 165-173 (1997)
[Publications] T.Ichinose and S.Takanobu: "Estimate of the difference between the Kac operator and the Schrodinger semigroup" Commun.Math Phys.vol.186. 167-197 (1997)
[Publications] T.Ichinose,A.Doumeki and H.Tamura: "Error bounds on exponential product formulas for Schrodinger operators" J.Math.Soc.Japan. vol.50. 359-377 (1998)
[Publications] T.Ichinose and H.Tamura: "Error estimates in operator norm for Trotter-Kato product formula" Integr.Equ.Oper.Theory. vol.27. 195-207 (1997)
[Publications] T.Ichinose and S.Takanobu: "The norm estimate of the difference between the Kac operator and the Schrodinger semigroup:A unified approach to the nonrelativistic and relativistic cases" Nagoya Math.J.vol.149. 53-81 (1998)
[Publications] T.Ichinose and H.Tamura: "Error bound in trace norm for Trotter-Kato product formula of Gibbs semigroups" Asymptotic Analysis. vol.17. 239-266 (1998)
[Publications] T.Ichinose and H.Tamura: "Error estimates in operator norm of exponential product formulas for propagators of parabolic evolution equations" Osaka Journal of Mathematics. vol.35. 751-770 (1998)
[Publications] T.Ichnose and S.Takanobu: "The norm estimate of the difference between the Kac operator and the Schrodinger semigroup II:Supplement to the relativistic case" Preprint.
[Publications] S.T.Kuroda and H.Nagatani: "Η_<-2>-construction and Hamiltonians with interactions of various type" スペクトル理論・散乱理論とその周辺,数理解析研究所講究録. vol.994. 155-167 (1997)
[Publications] S.T.Kuroda and H.Nagatani: "Η_<-2>-construction and some applications" Proc.Workshop.
[Publications] S.T.Kuroda and H.Nagatani: "Η_<-2>-constraction of general type and its application to point interactions" Preprint.
[Publications] A.Mizutani and T.Suzuki: "Finite element approximation of degenerate parabolic equations" Submitted.
[Publications] M.Suzuki,K.Watanabe: "Asymptotics of scattering phases for the Schrodinger operator with magnetic fields." Tokyo Journal of Mathematics. vol.20. 495-517 (1997)
[Publications] K.Watanabe: "Note on the spectral concentration for the Schrodinger operator with point interaction" SUT Journal of Mathematics.vol.34. 25-36 (1998)

1998 Fiscal Year Annual Research Report

汎関数解析

Principal Investigator

藤原 大輔 学習院大学, 理学部, 教授 (10011561)

Research Products

[Publications] D.Fujiwara and T.Tsuchida,: "The time slicing approximation of the fundamental solution for the Schrodinger equation with electromagnetic fields" Journal of the Math.Soc.Japan.vol.49. 299-327 (1997)

[Publications] D.Fujiwara,N.Kumano-go,K.Taniguchi: "A proof of estimates of Kumano-go-Taniguchi type for multiproduct of Fourier integral operators" Funkcialaj Ekvacioj. vol.40. 459-470 (1997)

[Publications] T.Ichinose and S.Takanobu: "On the norm estimate of the difference between the Kac operator and the Schrodinger semigroup" Differential Equations,Asymptotic Analysis and Mathematical Physics. vol.100. 165-173 (1997)

[Publications] T.Ichinose and S.Takanobu: "Estimate of the difference between the Kac operator and the Schrodinger semigroup" Commun.Math Phys.vol.186. 167-197 (1997)

[Publications] T.Ichinose,A.Doumeki and H.Tamura: "Error bounds on exponential product formulas for Schrodinger operators" J.Math.Soc.Japan. vol.50. 359-377 (1998)

[Publications] T.Ichinose and H.Tamura: "Error estimates in operator norm for Trotter-Kato product formula" Integr.Equ.Oper.Theory. vol.27. 195-207 (1997)

[Publications] T.Ichinose and S.Takanobu: "The norm estimate of the difference between the Kac operator and the Schrodinger semigroup:A unified approach to the nonrelativistic and relativistic cases" Nagoya Math.J.vol.149. 53-81 (1998)

[Publications] T.Ichinose and H.Tamura: "Error bound in trace norm for Trotter-Kato product formula of Gibbs semigroups" Asymptotic Analysis. vol.17. 239-266 (1998)

[Publications] T.Ichinose and H.Tamura: "Error estimates in operator norm of exponential product formulas for propagators of parabolic evolution equations" Osaka Journal of Mathematics. vol.35. 751-770 (1998)

[Publications] T.Ichnose and S.Takanobu: "The norm estimate of the difference between the Kac operator and the Schrodinger semigroup II:Supplement to the relativistic case" Preprint.

[Publications] S.T.Kuroda and H.Nagatani: "Η_<-2>-construction and Hamiltonians with interactions of various type" スペクトル理論・散乱理論とその周辺,数理解析研究所講究録. vol.994. 155-167 (1997)

[Publications] S.T.Kuroda and H.Nagatani: "Η_<-2>-construction and some applications" Proc.Workshop.

[Publications] S.T.Kuroda and H.Nagatani: "Η_<-2>-constraction of general type and its application to point interactions" Preprint.

[Publications] A.Mizutani and T.Suzuki: "Finite element approximation of degenerate parabolic equations" Submitted.

[Publications] M.Suzuki,K.Watanabe: "Asymptotics of scattering phases for the Schrodinger operator with magnetic fields." Tokyo Journal of Mathematics. vol.20. 495-517 (1997)

[Publications] K.Watanabe: "Note on the spectral concentration for the Schrodinger operator with point interaction" SUT Journal of Mathematics.vol.34. 25-36 (1998)

藤原大輔学習院大学, 理学部, 教授 (10011561)