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The Algebras of Bounded Analytic Functions on a Riemann Surface and the isomorphic problem

Research Project

Project/Area Number 12640147
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

HAYASHI Mikihiro  Hokkaido, Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (40007828)

Co-Investigator(Kenkyū-buntansha) NAGASAKA Yukio  Hokkaido, Univ., College of Medical Technology, Prof., 医療技術短期大学部, 教授 (50001855)
TACHIZAWA Kazuya  Hokkaido, Univ., Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (80227090)
NAKAZI Takahiko  Hokkaido, Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (30002174)
JIMBO Toshiya  Nara Univ. of Education, Fac. Of Educ., Prof., 教育学部, 教授 (80015560)
IZUCHI Keiji  Niigata Univ., Fac. Of Sci., Prof., 理学部, 教授 (80120963)
井上 純治  北海道大学, 大学院・理学研究科, 教授 (40000856)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2002: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2001: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2000: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsRieman surface / bounded analytic function / maximal ideal space / point separation problem / isomorphic problem / Hardy class / Myrberg phenomena / uniqueness theorem / 葉被覆面 / 有界正則関数環 / Hardy族 / Myrberg現象 / 2葉被覆面
Research Abstract

The algebra of all bounded analytic functions on a Riemann surface is of course determined by the Riemann surface. This converse is no longer obvious, and we call it the isomorphic problem. If a Riemann surface admits a meromorphic function bounded at the boundary of the surface and if bounded analytic functions separate the points of the surface, then the answer is yes. However, the investigator found a counter example when a surface admits no such meromorphic function.
When we ask the isomorphic problem, we assume that bounded analytic functions (weakly) separate the points of a surface, for otherwise isomorphic problem fails always. Thus, it is an interesting problem to determine whether a given surface is separating or not with respect to bounded analytic functions. This problem is also hard to solve in general. The investigator, together with Prof. Mitsuru Nakai and Dc. Yasuyuki Kobayashi, consider the case of a two-sheeted disc, where the projection of the sequence of ramification points converging to the center of the disc. We considered the case that a sequence of small discs centered at ramification points are removed, and found several sufficient conditions for separating and also not separating.

Report

(4 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (74 results)

All Other

All Publications (74 results)

  • [Publications] T.Nakazi: "The Nevanlinna counting functions for Rudin's orthogonal functions"Proc. Amer. Math. Soc.. (in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Nakazi: "Norms of some singular integral operators on weighted L^2 spaces"J.Operator Theory. (in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kazuya Tachizawa: "A generalization of the Lieb-Thirring inequalities in low dimensions"Hokkaido Mathematical Journal. (in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Izuchi: "K-hulls of QC-level sets"Indiana Univ.Math.J.. (in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Toshiya JIMBO: "Polynomial hulls of graphs of antiholomorphic functions"Scientiae Mathematicae Japonicae. 57・1. 121-127 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Nakazi: "Norm of a linear combination of two operators on a hilbert space"Bull. Austral. Math. Soc.. 65. 9-22 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Nakazi: "Two dimensional commutative Banach algebras and von Neumann Inequality"Linear Alg. Appl.. 341. 273-290 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kazuya Tachizawa: "On the moments of the negative eigenvalues of elliptic operators"Journal of Fourier Analysis and Applications. 8. 233-244 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Izuchi: "On ideals in H^∞ whose closures are intersections of maximal ideals"Michigan Math. J.. 50・1. 3-16 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 神保敏弥: "多重調和関数のグラフの多項式凸包"数理解析研究所講究録. 1277. 136-140 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Nakazi: "Toeplitz operators and weighted norm inequalities on the bidisc"Math.Ineq.and Appl.. 4. 429-441 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K.Izuchi: "Trivial points in the maximal ideal space of H^∞.III"Houston J. Math.. 27. 873-881 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Hayashi: "A uniqueness theorem and the Myrberg phenomenon for a Zalcman domain"J. d'Analyse Math.. 82. 267-283 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 林 実樹廣: "A uniqueness theorem and the Myrberg phenomenon for a Zalcman domain (I)"数理解析研究所講究録. 1137. 19-25 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 林 実樹廣: "A uniqueness theorem and the Myrberg phenomenon for a Zalcman domain (II)"数理解析研究所講究録. 1137. 26-32 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Nakazi: "Compact Toeplitz operators with continuous symbols on weighted Bergman spaces"Glasgow J.Math.. 42. 31-35 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J.Inoue: "On the Zeros of Solutions of an Extremal Problem in H^1"Complex Variables. 40. 173-188 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Pamela Gorkin: "Higher order hulls in H^∞. II"J. Funct. Anal.. 177. 107-129 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 林 実樹廣: "複素関数論概論"サイエンス社(in press). 230 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Nakazi: "The Nevanlinna counting functions for Rudin's orthogonal functions"Proc. Amer. Math. Soc.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Nakazi: "Norms of some singular integral operators on weighted L^2 spaces"J. Operator Theory. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kazuya Tachizawa: "A generalization of the Lieb-Thirring inequalities in low dimensions"Hokkaido Mathematical Journal. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Izuchi: "K-hulls of QC-level sets"Indiana Univ. Math. J.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Toshiya JIMBO: "Polynomial hulls of graphs of antiholomorphic functions"Scientiae Mathematicae Japonicae. 57. 121-127 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Nakazi: "Norm of a linear combination of two operators on a Hilbert space"Bull. Austral. Math. Soc.. 65. 9-22 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Nakazi: "Two dimensional commutative Banach algebras and von Neumann Inequality"Linear Alg. Appl.. 341. 273-290 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kazuya Tachizawa: "On the moments of the negative eigenvalues of elliptic operators"Journal of Fourier Analysis and Applications. 8. 233-244 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Izuchi: "On ideals in H^∞ whose closures are intersections of maximal ideals"Michigan Math. J.. 50. 3-16 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Toshiya JIMBO: "The polynomial convex hull of the graph of a pluriharmonic function (in Japanese)"RIMS, Kokyuroku. No. 1277. 136-140 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Nakazi: "Toeplitz operators and weighted norm inequalities on the bidisc"Math. Ineq. And Appl.. 4. 429-441 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] K. Izuchi: "Trivial points in the maximal ideal space of H^∞. III"Houston J. Math.. 27. 873-881 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M. Hayashi: "A uniqueness theorem and the Myrberg phenomenon for a Zalcman domain"J. d'Analyse Math.. 82. 267-283 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M. Hayashi: "A uniqueness theorem and the Myrberg phenomenon for a Zalcman domain (I) (in Japanese)"RIMS, Kokyuroku. No. 1137. 19-25 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M. Hayashi: "A uniqueness theorem and the Myrberg phenomenon for a Zalcman doman (II) (in Japanese)"RIMS, Kokyuroku. No. 1137. 26-32 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Nakazi: "Compact Toeplitz operators with continuous symbols on weighted Bergman spaces"Glasgow J. Math.. 42. 31-35 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] J. Inoue: "On the Zeros of solutions of an extremal problem in H^1"Complex Variables. 40. 173-188 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Pamela Gorkin: "Higher order hulls in H^∞. II"J. Funct. Anal.. 177. 107-129 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M. Hayashi: "Theory of Complex Function Theory (in Japanese)"Saiensu-sha(in press). 230 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Nakazi: "The Nevanlinna counting functions for Rudin's orthogonal functions"Proc. Amer. Math. Soc.. (in press).

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Nakazi: "Norms of some singular integral operators on weighted L^2 spaces"J. Operator Theory. (in press).

    • Related Report
      2002 Annual Research Report
  • [Publications] Kazuya Tachizawa: "A generalization of the Lieb-Thirring inequalities in low dimensions"Hokkaido Mathematical Journal. (in press).

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Izuchi: "K-hulls of QC-level sets"Indiana Univ. Math. J.. (in press).

    • Related Report
      2002 Annual Research Report
  • [Publications] Toshiya JIMBO: "Polynomial hulls of graphs of antiholomorphic functions"Scientiae Mathematicae Japonicae. 57・1. 121-127 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Nakazi: "Norm of a linear combination of two operators on a Hilbert space"Bull. Austral. Math. Soc.. 65. 9-22 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Nakazi: "Two dimensional commutative Banach algebras and von Neumann Inequality"Linear Alg. Appl.. 341. 273-290 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kazuya Tachizawa: "On the moments of the negative eigenvalues of elliptic operators"Journal of Fourier Analysis and Applications. 8. 233-244 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] J.Inoue: "Bochner-Schoenberg-Eberlein type extension of measure algebras and its application"Seminar on functions Spaces, 2001. 74-78 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Izuchi: "On ideals in H^∞ whose closures are intersections of maximal ideals"Michigan Math. J.. 50・1. 3-16 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 神保敏弥: "多重調和関数のグラフの多項式凸包"数理解析研究所講究録. 1277. 136-140 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 林 実樹廣: "複素関数論概論"サイエンス社(in press). 230 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] M. Hayashi: "A uniqueness theorem and the Myrberg type phenomenon for a Zalcman domain"J. d'Analyse Math.. 82. 267-283 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] J. Inoue: "On the zeros of an extremal problem in H^1"Complex Variables Theory Appl.. 40. 173-188 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] T. Nakazi: "Compact Toeplitz operators with continuous symbols on weighted Bergman spaces"Glasgow J. Math.. 42. 31-35 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] T. Nakazi: "Norm inequalities for some singular integral operators"Math. Ineq. and Appl.. 3. 411-421 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] T. Nakazi: "Two dimensional Q-algebras"Linear Alg. Appl.. 315. 197-205 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] T. Nakazi: "Finite rank intermediate Hankel operators on the Bergman space"International J. Math and Math. Sci.. 25. 19-31 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T. Nakazi: "Toeplitz operators and weighted norm inequalities on the bidisc"Math. Ineq. and Appl.. 4. 429-441 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T. Nakazi: "Functions in N+ with the positive real parts on the boundary, and extremal problems in H^1"Complex Valiables Theory Appl.. 44. 259-279 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] G. Hirasawa: "Korovkin type approximation theorems on the disk algebra"Hokkaido Math. J.. 29. 103-117 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] K. Izuchi: "Spreading Blaschke products and homeomorphic parts"Complex Variables Theory Appl.. 40. 359-369 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] P. Gorkin: "Higher order hulls in H^∞. II."J. Funct. Anal.. 177. 107-129 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] K. Izuchi: "Douglas algebras which admit codimension 1 linear isometries"Proc. Amer. Math. Soc.. 129. 2069-2074 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] K. Izuchi: "Singular inner functions of L^1-type. II."J. Math. Soc. Japan. 53. 285-305 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] K. Izuchi: "Trivial points in the maximal ideal space of H^∞. III."Houston J. Math.. (in press).

    • Related Report
      2001 Annual Research Report
  • [Publications] K. Izuchi: "Outer and inner vanishing measures and division in H^∞+C"Revista Mate. Iberoamericana. (in press).

    • Related Report
      2001 Annual Research Report
  • [Publications] K. Izuchi: "On ideals in H^∞ whose closures are intersections of maximal ideals"Michigan Math. J.. (in press).

    • Related Report
      2001 Annual Research Report
  • [Publications] K. Izuchi: "K-hulls of QC-level sets"Indiana Univ. Math. J.. (in press).

    • Related Report
      2001 Annual Research Report
  • [Publications] T. Hosokawa: "Isolated points and essential components of Composition Operators on H^∞"Proc. Amer. Math. Soc.. (in press).

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Hayashi: "A uniquenss theorem and the Myrbery type phenomenon for a Zalcman domain"J.d'Analyse Math.. 82. 267-283 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] J.Inoue: "On the zeros of an extremal problem in H^1"Complex Veriablex. 40. 173-188 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Nakazi: "On as invariant subspace whose common zero set is the zeros of some function"Nihonkai Math.J.. 11. 1-9 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Nakazi: "Norm inequalities for some singular integral operators"Math.Ineq.and Appl.. 3. 411-421 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] P.Gorkin: "Higher order hulls in H^∞ II"J.Functional Anal.. 177. 107-129 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Izuchi: "Trivial points in the maximal ideal"Houston J.Math. (印刷中).

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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