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トーラス上の不変部分空間の構造

Research Project

Project/Area Number 07640183
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionNiigata University

Principal Investigator

泉池 敬司  新潟大学, 理学部, 教授 (80120963)

Co-Investigator(Kenkyū-buntansha) 松本 和子  新潟大学, 大学院・自然科学研究科, 助手 (60239093)
浅野 和雄  新潟大学, 理学部, 講師 (80000876)
羽鳥 理  新潟大学, 大学院・自然科学研究科, 助教授 (70156363)
関川 浩永  新潟大学, 理学部, 教授 (60018661)
斉藤 吉助  新潟大学, 理学部, 教授 (30018949)
Project Period (FY) 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1995: ¥2,000,000 (Direct Cost: ¥2,000,000)
Keywords不変部分空間 / ブルゲン環 / 極大イデアル空間 / ブラシュケ積 / BKW-作用素 / 作用素環 / ケーラー多様体 / レビ問題
Research Abstract

研究目的であった,乗法作用素Vz,Vw,Vz^*,Vw^*の多項式として得られる作用素の性質を利用して,トーラス上の不変部分空間の構造の完全決定までには至らなかった。しなしながら,真次氏,大野氏との共同研究により,今までの研究を更に押し進めることができた(投稿中)。そして,今後不変部分空間の構造と深く関係してくると思われるBKW-作用素の研究をスタートさせることができた。又トーラス上のハ-ディ空間の研究はブルゲン環を通して,かなりの成果が上げられた。
研究組織全体的には,活発に研究を進展させることができた。個別には
(1)斉藤:Jonesの指数が4以下の時,subdiagonal環の存在問題を解決した。
(2)関川:4次元コンパクト,概ケーラー局所対称空間はケーラー多様体となることを示した。
(3)羽鳥:コンパクト・アーベル群上のp-gmultiplier環の極大イデアル空間を決定した。
(4)松本:Stein多様体等の中の滑らかな境界を持つ部分領域に対しては,弱い意味のg-Levi問題を肯定的に解決した。

Report

(1 results)
  • 1995 Annual Research Report
  • Research Products

    (19 results)

All Other

All Publications (19 results)

  • [Publications] P. Gorkin.: "Bourgain algebras on the maximal ideal space of H^∞" Rocky Mountain J. Math.25. 1025-1051 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Izuchi: "Multipliers and Bourgain algebras of H^∞+C on the polydisk" Pacific J. Math.171. 167-208 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Izuchi: "BKW-operators on the polydis and ball algebras" Far East J. Math. Sci.(発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Izuchi: "Bourgain algebras of spaces of n-harmonic functions in the unit polydisk" Canadian Math. Bull.(発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Izuchi: "Sequential BKW-operators and function algebras" J. Approxiwation Theory. (発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Izuchi: "BKW-operators on the lnterval and the sequence. spaces" J. Approxiwation Theory. (発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] C. Guillory: "Interpolating Blaschke product of type G" Complex Variables. (発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Sekigawa: "Curvature homogeneity of fouv-diwensional manifolds" J. Korean Math. J.32. 93-101 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Sekigawa: "Compact Hermitian surfaces of pointwise constant holomorphic sectional curvature" Glasgow Math. J.37. 343-349 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] H. Hashimoto: "Miniwal surfaces in a 4-dimensional sphere" Houston J. Math.21. 449-464 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T. Oguro: "Almost Kahler structures on the Riemannian product of a 3-dimensional hyperbolic space and a real line" Tsukuba J. Math.(発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] N. Murakoshi: "Four-dimensional almost Kahler locally symmetric spaces" Differential geometry and its applications. (発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] J. T. Cho: "Volume-preserving geodesic Symmetries on four-dimensional Hermitian Einstein spaces" Nagoya Math. J.(発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] K.-S. Saito: "Generalized interpolation in finite maximal subdiagonal algebras" Math. Proc. Camb. Philo. Soc.117. 11-20 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] K.-S. Saito: "Subdiagonal algebras for subfactors II" Canadian Math. Bull.(発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] O. Hatori: "A characterization of Lacunary sets and spectral properties of Fourier multipliers" Lecture Notes in Pure and Applied Math.172. 183-203 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] O. Hatori: "Functions which operate on algebras of Fourier multiplers" Tohoku Math. J.47. 105-115 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Matsumoto: "Boundary distance functions and g-convexity of pseudo convex domains of general order in kahler manifolds" J. Math. Soc. Japan. 48. 85-107 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] K. Matusmoto: "Boundary distance functions and q-convexity of locally q-convexdomains with cormers in kahler manifolds" Geometric Complex Analysis world Sci. Publishing. (発表予定). (1996)

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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