1999 Fiscal Year Annual Research Report

実解析と関数解析の総合的研究

Research Project

Project/Area Number	11304009
Research Category	Grant-in-Aid for Scientific Research (A)
Research Institution	Tokyo Woman's Christian University
Principal Investigator	宮地晶彦東京女子大学, 文理学部, 教授 (60107696)
Co-Investigator(Kenkyū-buntansha)	片山良一大阪教育大学, 教育学部, 教授 (10093395) 若山正人九州大学, 大学院・数理学研究科, 教授 (40201149) 小林和夫早稲田大学, 教育学部, 教授 (30139589) 大矢雅則東京理科大学, 理工学部, 教授 (90112896) 田島慎一新潟大学, 工学部, 助教授 (70155076)
Keywords	Hardy空間 / 特異積分 / Navier-Stokes方程式 / 相転移 / ホロノミック系 / Turnbull等式 / Putnam不等式 / Jaynes-Cummingsモデル
Research Abstract	実解析そのものの研究では、最大関数による重み付きHardy空間の理論の一般化、多重線形作用素のHardy空間での有界性の証明、Littlewood-Paley関数などの精密な評価、rough kernelをもつ特異積分作用素の有界性の証明、などにおいて成果があり、宮地、薮田、佐藤らが研究をまとめた。また、階数1の半単純Lie群上で最大関数とHardy空間の研究を、河添がまとめた。偏微分方程式の研究では、実解析および関数解析分野の研究成果を応用して、Hardy空間などを利用した半空間でのStokes flowの研究、Navier-Stokes方程式の初期値問題で初速度が無限遠で減少しない場合の時間大域解の存在証明、2成分合金の相分離現象を記述する方程式の提出、非線形方程式の慣性多様体のC^1近似、などに成果があり、儀我、剣持、小林らが研究をまとめた。他に、代数解析の理論と手法をも利用したホロノミック系の初期値問題の解法、Dirac方程式の一意接続性の研究、などの成果を田島、大阿久、大鍛冶らがまとめた。表現論関係で、Pfaffianに関する総和公式、歪対象行列のTurnbull等式の研究、などに成果があり、若山、梅田らが成果をまとめた。実解析と関数解析の成果を函数環や作用素環、作用素論などに応用して、p-hyponormal作用素の種々の性質、Putnam不等式とXiaスペクトル、などの研究に成果があり、長らがまとめた。エントロピーや容量などの理論を量子情報理論へ応用して、Jaynes-Cummingsモデルなどの研究を行い、大矢らが研究成果をまとめた。

Research Products

(25 results)

All Other

All Publications (25 results)

[Publications] Akihiko Miyachi: "Hardy space estimate for the product of singular integrals"Canadian Journal of Mathematics. (掲載予定).
[Publications] Akihiko Miyachi: "Weighted Hardy spaces on a domain"Proceedings of the Second Congress ISAAC. (掲載予定).
[Publications] P.Sarnak & M.Wakayama: "Equidistribution of holonomy about closed geodesics"Duke Mathematical Journal. 100. 1-57 (1999)
[Publications] M.Ishikawa & M.Wakayama: "Applications of minor summation formulas II, Pfaffians and Shur polynomials"Joural of Combinatorial Theory Series A. 88. 136-157 (1999)
[Publications] S.Tajima & Y.Nakamura: "Residue calculus with differential operators"Kyushu Journal of Mathematics. 53(掲載予定). (1999)
[Publications] Shin-ichi Tajima: "Algebraic analysis of multivariate Hermite interpolation formulas"Proceedings of Second Congress ISAAC. (掲載予定).
[Publications] Kazuo Kobayasi: "C' approximations of inertial manifolds via finite differences"Proceedings of American Mathematical Society. 127巻4号. 1143-1150 (1999)
[Publications] Kazuo Kobayasi: "C' approximations of invariant manifolds for semilinear PPEs and applications"Proceedings of the 8th International Conference on Free Boundary Problem. 103 (1999)
[Publications] L.Accardi and M.Ohya: "Compound channels, transition expectations, and liftings"Appl. Math. Optim.. 39. 33-59 (1999)
[Publications] Masanori Ohya: "Fundamentals of quantum mutual entropy and capacity"Open System and Information Dynamics. 6巻1号. 69-78 (1999)
[Publications] L.D.Carli and Takashi Okaji: "Strong unique continuation property for the Dirac equation"Publ. Res. Inst. Math. Sci. Kyoto Univ.. 35巻6号. 825-846 (1999)
[Publications] Nobuyuki Kenmochi & M.Kubo: "Weak solutions of nonlinear systems for non-isothermal phase transitions"Adv. Math. Sci. Appl.. 9. 499-521 (1999)
[Publications] A.Damlamian & N.Kenmochi: "Evolution equations associated with non-isothermal phase separation: Subdifferential approach"Ann. Mat. Pura Appl.. 176. 167-190 (1999)
[Publications] Toru Umeda: "On Turnbull identity for skew symmetric matrices"Proc. Edinburgh Math. Soc.. (掲載予定).
[Publications] Takeshi Kawazoe: "Hardy spaces and maximal operators on real vank 1 semisimple Lie groups I"Tohoku Math. Journal. 52(掲載予定). (2000)
[Publications] Y.Giga,S.Matsui, and Y,Shimizu: "On estimates in Hardy space for the Stokes flow in a half space"Mathematische Zeitschrift. 231. 383-396 (1999)
[Publications] Y.Giga,K.Inui, and S.Matsui: "On the Canchy problem for the Navier-Stokes equations with nondecaying intial data"Quaderni di Matematica. 4. 27-67 (1999)
[Publications] Y.Sakamoto and Kozo Yabuta: "Boundedness of Marcinkiewicz funetions"Studia Mathematica. 135. 103-142 (1999)
[Publications] 田中純一: "概周期関数の拡張と流れの上の解析性"数学. 51巻2号. 113-128 (1999)
[Publications] Muneo Cho and Yoshihiko Nagano: "Simple proof of the p-hyponormality of the Aluthge transformations"Integr. Equat. Oper. Th.. 33. 248-251 (1999)
[Publications] Muneo Cho and Tadasi Huruya: "Putnam's inequality for p-hyponormal n-tuples"Glasgow Math. Journal. 41. 13-17 (1999)
[Publications] Masanori Ohya & S.Furuichi: "Quantum mutual entropy for Jaynes-Cummings model"Reports on Mathematical Physics. 44. 81-86 (1999)
[Publications] 儀我美一・儀我美保: "非線形偏微分方程式-解の漸近挙動と自己相似解-"共立出版. 300 (1999)
[Publications] 梅田亨,黒川信重,若山正人,中島さち子: "ゼータの世界"日本評論社. (1999)
[Publications] 大矢雅則: "量子コンピュータの数理"丸善株式会社. (1999)

1999 Fiscal Year Annual Research Report

実解析と関数解析の総合的研究

Principal Investigator

宮地 晶彦 東京女子大学, 文理学部, 教授 (60107696)

Research Products

[Publications] Akihiko Miyachi: "Hardy space estimate for the product of singular integrals"Canadian Journal of Mathematics. (掲載予定).

[Publications] Akihiko Miyachi: "Weighted Hardy spaces on a domain"Proceedings of the Second Congress ISAAC. (掲載予定).

[Publications] P.Sarnak & M.Wakayama: "Equidistribution of holonomy about closed geodesics"Duke Mathematical Journal. 100. 1-57 (1999)

[Publications] M.Ishikawa & M.Wakayama: "Applications of minor summation formulas II, Pfaffians and Shur polynomials"Joural of Combinatorial Theory Series A. 88. 136-157 (1999)

[Publications] S.Tajima & Y.Nakamura: "Residue calculus with differential operators"Kyushu Journal of Mathematics. 53(掲載予定). (1999)

[Publications] Shin-ichi Tajima: "Algebraic analysis of multivariate Hermite interpolation formulas"Proceedings of Second Congress ISAAC. (掲載予定).

[Publications] Kazuo Kobayasi: "C' approximations of inertial manifolds via finite differences"Proceedings of American Mathematical Society. 127巻4号. 1143-1150 (1999)

[Publications] Kazuo Kobayasi: "C' approximations of invariant manifolds for semilinear PPEs and applications"Proceedings of the 8th International Conference on Free Boundary Problem. 103 (1999)

[Publications] L.Accardi and M.Ohya: "Compound channels, transition expectations, and liftings"Appl. Math. Optim.. 39. 33-59 (1999)

[Publications] Masanori Ohya: "Fundamentals of quantum mutual entropy and capacity"Open System and Information Dynamics. 6巻1号. 69-78 (1999)

[Publications] L.D.Carli and Takashi Okaji: "Strong unique continuation property for the Dirac equation"Publ. Res. Inst. Math. Sci. Kyoto Univ.. 35巻6号. 825-846 (1999)

[Publications] Nobuyuki Kenmochi & M.Kubo: "Weak solutions of nonlinear systems for non-isothermal phase transitions"Adv. Math. Sci. Appl.. 9. 499-521 (1999)

[Publications] A.Damlamian & N.Kenmochi: "Evolution equations associated with non-isothermal phase separation: Subdifferential approach"Ann. Mat. Pura Appl.. 176. 167-190 (1999)

[Publications] Toru Umeda: "On Turnbull identity for skew symmetric matrices"Proc. Edinburgh Math. Soc.. (掲載予定).

[Publications] Takeshi Kawazoe: "Hardy spaces and maximal operators on real vank 1 semisimple Lie groups I"Tohoku Math. Journal. 52(掲載予定). (2000)

[Publications] Y.Giga,S.Matsui, and Y,Shimizu: "On estimates in Hardy space for the Stokes flow in a half space"Mathematische Zeitschrift. 231. 383-396 (1999)

[Publications] Y.Giga,K.Inui, and S.Matsui: "On the Canchy problem for the Navier-Stokes equations with nondecaying intial data"Quaderni di Matematica. 4. 27-67 (1999)

[Publications] Y.Sakamoto and Kozo Yabuta: "Boundedness of Marcinkiewicz funetions"Studia Mathematica. 135. 103-142 (1999)

[Publications] 田中 純一: "概周期関数の拡張と流れの上の解析性"数学. 51巻2号. 113-128 (1999)

[Publications] Muneo Cho and Yoshihiko Nagano: "Simple proof of the p-hyponormality of the Aluthge transformations"Integr. Equat. Oper. Th.. 33. 248-251 (1999)

[Publications] Muneo Cho and Tadasi Huruya: "Putnam's inequality for p-hyponormal n-tuples"Glasgow Math. Journal. 41. 13-17 (1999)

[Publications] Masanori Ohya & S.Furuichi: "Quantum mutual entropy for Jaynes-Cummings model"Reports on Mathematical Physics. 44. 81-86 (1999)

[Publications] 儀我美一・儀我美保: "非線形偏微分方程式-解の漸近挙動と自己相似解-"共立出版. 300 (1999)

[Publications] 梅田亨,黒川信重,若山正人,中島さち子: "ゼータの世界"日本評論社. (1999)

[Publications] 大矢雅則: "量子コンピュータの数理"丸善株式会社. (1999)

宮地晶彦東京女子大学, 文理学部, 教授 (60107696)

[Publications] 田中純一: "概周期関数の拡張と流れの上の解析性"数学. 51巻2号. 113-128 (1999)