1995 Fiscal Year Annual Research Report

トーラス上の不変部分空間の構造

Research Project

Project/Area Number	07640183
Research Institution	Niigata 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)
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。

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)
[Publications] K. Izuchi: "Multipliers and Bourgain algebras of H^∞+C on the polydisk" Pacific J. Math.171. 167-208 (1995)
[Publications] K. Izuchi: "BKW-operators on the polydis and ball algebras" Far East J. Math. Sci.(発表予定).
[Publications] K. Izuchi: "Bourgain algebras of spaces of n-harmonic functions in the unit polydisk" Canadian Math. Bull.(発表予定).
[Publications] K. Izuchi: "Sequential BKW-operators and function algebras" J. Approxiwation Theory. (発表予定).
[Publications] K. Izuchi: "BKW-operators on the lnterval and the sequence. spaces" J. Approxiwation Theory. (発表予定).
[Publications] C. Guillory: "Interpolating Blaschke product of type G" Complex Variables. (発表予定).
[Publications] K. Sekigawa: "Curvature homogeneity of fouv-diwensional manifolds" J. Korean Math. J.32. 93-101 (1995)
[Publications] K. Sekigawa: "Compact Hermitian surfaces of pointwise constant holomorphic sectional curvature" Glasgow Math. J.37. 343-349 (1995)
[Publications] H. Hashimoto: "Miniwal surfaces in a 4-dimensional sphere" Houston J. Math.21. 449-464 (1995)
[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).
[Publications] N. Murakoshi: "Four-dimensional almost Kahler locally symmetric spaces" Differential geometry and its applications. (発表予定).
[Publications] J. T. Cho: "Volume-preserving geodesic Symmetries on four-dimensional Hermitian Einstein spaces" Nagoya Math. J.(発表予定).
[Publications] K.-S. Saito: "Generalized interpolation in finite maximal subdiagonal algebras" Math. Proc. Camb. Philo. Soc.117. 11-20 (1995)
[Publications] K.-S. Saito: "Subdiagonal algebras for subfactors II" Canadian Math. Bull.(発表予定).
[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)
[Publications] O. Hatori: "Functions which operate on algebras of Fourier multiplers" Tohoku Math. J.47. 105-115 (1995)
[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)
[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)

1995 Fiscal Year Annual Research Report

トーラス上の不変部分空間の構造

Principal Investigator

泉池 敬司 新潟大学, 理学部, 教授 (80120963)

Research Products

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

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

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

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

[Publications] K. Izuchi: "Sequential BKW-operators and function algebras" J. Approxiwation Theory. (発表予定).

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

[Publications] C. Guillory: "Interpolating Blaschke product of type G" Complex Variables. (発表予定).

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

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

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

[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).

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

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

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

[Publications] K.-S. Saito: "Subdiagonal algebras for subfactors II" Canadian Math. Bull.(発表予定).

[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)

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

[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)

[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)

泉池敬司新潟大学, 理学部, 教授 (80120963)