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Functional Analyistic Studies On The Algebra Of Bounded Analytic Functions On A Riemann Surface

Research Project

Project/Area Number 16540132
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 University, Fac. of Sci, Professor (40007828)

Co-Investigator(Kenkyū-buntansha) NAKAZI Takahiko  Hokkaido University, Fac. of Sci., Professor (30002174)
TACHIZAWA Kazuya  Hokkaido University, Fac. of Sci., Associate Professor (80227090)
NAGASAKA Yukio  Hokkaido University, Fac. of Sci., Professor (50001855)
IZUCHI Keiji  Niigata University, Dept. of Math., Professor (80120963)
SEGAWA Shigeo  Daido Inst., Dept. of Math., Professor (80105634)
Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,870,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsbounded analytic function / maximal ideal space / Riemann surface / pole set / Shilov boundary / Hardy class / composition operator / invariant subspace / 補間問題 / 同型問題 / pole集合
Research Abstract

1. Studies on Riemann surfaces and bounded analytic functions and harmonic functions on them:
In the case that a given Riemann surface is not included openly and homeomorphically in the maximal ideal space of the algebra of all bounded analytic functions, we find a condition on a Riemann surface whose Shilov boundary is totally disconeccted. This result can be applied to the uniqueness theorem of linear extremal problem. Also, we studied the structure of the fibre in the maximal ideal space. In addition, we show that Royden's resolution of a Riemann surface can be constructed by the method of simultaneous analytic continuation of a give family of meromorphic functions.
We studied on relations between the Martin boundary and harmonic functions. We succeeded in a characterization for the existence of Green functions on a infinite-sheeted covering Riemann surface over the Riemann sphere, that is obtained by pasting a pair of sheets along each curve in a given sequence of curves, in terms of the sequence of capacities of curves.
2. Stuies on Hardy classes and the function theory of several variables:
We give the best possible estimate of the norm of cross-commutators of two subnormal operators by means of spectral area, and generalized a former result to the case of p-quasi normal operators.
We give a characterization of weighted Herz space by means of wavelets. Our result correct an error in the result published by Tang-Yang in 2000, and further showed that our system of wavelets form an unconditional basis.
We gave a new type of factorization of an inner function in relation of connected components of the zero of the inner function, which solves a problem posed in a paper published in 2004. We also studies when a linear combination of composition operators is compact for an analytic function space.

Report

(5 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (59 results)

All 2008 2007 2006 2005 2004

All Journal Article (51 results) (of which Peer Reviewed: 20 results) Presentation (8 results)

  • [Journal Article] Linear combinations of composition operators on H^\infty2008

    • Author(s)
      Izuchi, K.
    • Journal Title

      J. Math. Anal. Appl. 33

      Pages: 820-839

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Linear combinations of composition operators on H^\infty2008

    • Author(s)
      Izuchi, K.
    • Journal Title

      J. Math. Anal. Appl 33

      Pages: 820-839

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Shift operators on the C^2-valued Hardy spaces2007

    • Author(s)
      Douglas, R.G.
    • Journal Title

      Acta Sci. Math. (Szeged) 73

      Pages: 729-744

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Spectral area estimates for norms of commutators2007

    • Author(s)
      Cho, M.
    • Journal Title

      J. Korean Math. Soc. 44

      Pages: 855-861

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Singular inner functions whose Frostman shifts are Carleson-Newman Blaschke products II2007

    • Author(s)
      Izuchi, K.
    • Journal Title

      Complex Var. Elliptic Equ. 52

      Pages: 425-437

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Common zero sets of equivalent singular inner functions II2007

    • Author(s)
      Izuchi, K.
    • Journal Title

      Studia Math. 180

      Pages: 133-142

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] The role of symmetry for pasting arcs in the type problems2007

    • Author(s)
      Nakai, M.
    • Journal Title

      Complex Var. Elliptic Equ. 52

      Pages: 1161-1169

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Shift operators on the C^2-valued Hardy spaces2007

    • Author(s)
      Douglas, R. G.
    • Journal Title

      Acta Sci. Math. (Szeged) 73

      Pages: 729-744

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Spectral area estimates for norms of commutators2007

    • Author(s)
      Cho, M.
    • Journal Title

      J. Korean Math. Soc 44

      Pages: 855-861

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Singular inner functions whose Frostman shifts are Carleson-Newman Blaschke products II2007

    • Author(s)
      Izuchi, K.
    • Journal Title

      Complex Var. Elliptic Equ 52

      Pages: 425-437

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Common zero sets of equivalent singular inner functions II2007

    • Author(s)
      Izuchi, K.
    • Journal Title

      Studia Math 180

      Pages: 133-142

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] The role of symmetry for pasting arcs in the type problems2007

    • Author(s)
      Nakai, M.
    • Journal Title

      Complex Var. Elliptic Equ 52

      Pages: 1161-1169

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Shift operators on the C^2-valued Hardy spaces2007

    • Author(s)
      Douglas, R. G.
    • Journal Title

      Acta Sci. Math.(Seged) 73

      Pages: 729-744

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a problem about the Shilov boundary of a Riemann surface2006

    • Author(s)
      林, 実樹廣
    • Journal Title

      数理解析研究所講究録 1519

      Pages: 59-70

    • NAID

      110004848995

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2006 Annual Research Report
  • [Journal Article] Double commuting compresset shifts and generalized interpolation in the Hardy space over the bidisc2006

    • Author(s)
      Nakazi, Takahiko
    • Journal Title

      Inegr. equ. operator theory 56

      Pages: 543-558

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2006 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Isometric composition operators between two weighted Hardy spaces2006

    • Author(s)
      Nakazi, Takahiko
    • Journal Title

      Nihonkai Math. J. 17

      Pages: 111-124

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2006 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic Riemann surfaces without unbounded positive haromic functions2006

    • Author(s)
      Masaoka, H.
    • Journal Title

      Advanced Studies in Pure Math. 44

      Pages: 227-232

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Cross commutators on backward shift invariant subspaces over the bidisk2006

    • Author(s)
      Izuchi, Kei Ji
    • Journal Title

      Acta Sci. Math. (Szeged) 72no.1-2

      Pages: 251-270

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Singular inner functions whose Frostman shifts are Carleson-Newman Blaschke products2006

    • Author(s)
      Izuchi, Keiji
    • Journal Title

      Complex Var. Elliptic Equ. 51no.3

      Pages: 255-266

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On a problem about the Shilov boundary of a Riemann surface2006

    • Author(s)
      Hayashi, Mikihiro
    • Journal Title

      RIMS Kokyuroku 1519

      Pages: 59-70

    • NAID

      110004848995

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Isometric composition operators between two weighted Hardy spaces2006

    • Author(s)
      Nakazi, Takahiko
    • Journal Title

      Nihonkai Math. J 17

      Pages: 111-124

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Hyperbolic Riemann surfaces without unbounded positive haromic functions2006

    • Author(s)
      Masaoka, H.
    • Journal Title

      Advanced Studies in Pure Math 44

      Pages: 227-232

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Cross commutators on backward shift invariant subspaces over the bidisk2006

    • Author(s)
      Izuchi, Kei Ji
    • Journal Title

      Acta Sci. Math. (Szeged) 72 no. 1-2

      Pages: 251-270

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Singular inner functions whose Frostman shifts are Carleson-Newman Blaschke products2006

    • Author(s)
      Izuchi, Keiji
    • Journal Title

      Complex Var. Elliptic Equ 51 no. 3

      Pages: 255-266

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Hyperbolic Riemann surfaces without unbounded positive haromic functions2006

    • Author(s)
      Masaoka, H.
    • Journal Title

      Advanced Studies in Pure Mathematics 44

      Pages: 227-232

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Cross commutators on backward shift invariant subspaces over the bidisk2006

    • Author(s)
      Izuchi, KeiJi
    • Journal Title

      Acta Sci. Math. (Szeged) 72・1-2

      Pages: 251-270

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Singular inner functions whose Frostman shifts are Carleson-Newman Blaschke products2006

    • Author(s)
      Izuchi, KeiJi
    • Journal Title

      Complex Var. Elliptic Equ. 51・3

      Pages: 255-266

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Weighted Sobolev-Lieb-Thirring inequalities2005

    • Author(s)
      Tachizawa, Kazuya
    • Journal Title

      Rev. Mat. Iberoamericana 21

      Pages: 67-85

    • NAID

      120006456909

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Interpolation of weighted l^p sequences by H^p functions2005

    • Author(s)
      Nakazi, Takahiko
    • Journal Title

      Taiwanese Journal of Mathematics 9no.3

      Pages: 457-467

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Rouche type theorems and a theorem of Adamyan, Arov and Krein2005

    • Author(s)
      Nakazi, Takahiko
    • Journal Title

      Mathematica Scandiavica 97

      Pages: 154-160

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2005 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compact perturbations of Hankel Operators2005

    • Author(s)
      Chen, Xiaoman
    • Journal Title

      J. Reine Angew. Math. 51no.1

      Pages: 1-48

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On a class of closed prime ideals in H^\infty2005

    • Author(s)
      Izuchi, Keiji
    • Journal Title

      Complex Variables 50no.13

      Pages: 1011-1023

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Quasiconformal mappings and minimal Martin boundary of p-sheeted unlimited covering surfaces of the complex plane2005

    • Author(s)
      Masaoka, H.
    • Journal Title

      Kodai Math. J. 28no.2

      Pages: 275-279

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Weighted Sobolev-Lieb-Thirring inequalities2005

    • Author(s)
      Tacbizawa, Kazuya
    • Journal Title

      Rev. Mat. Iberoamericana 21

      Pages: 67-85

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Interpolation of weighted 1^p sequences by H^p functions2005

    • Author(s)
      Nakazi, Takahiko
    • Journal Title

      Taiwanese Journal of Mathematics 9 no. 3

      Pages: 457-467

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Compact perturbations of Hankel Operators2005

    • Author(s)
      Chen, Xiaoman
    • Journal Title

      J. Reine Angew. Math 51 no. 1

      Pages: 1-48

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On a class of closed prime ideals in H^\infty2005

    • Author(s)
      Izuchi, Keiji
    • Journal Title

      Complex Variables 50 no. 13

      Pages: 1011-1023

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Quasiconformal mappings and minimal Martin boundary of p-sheeted unlimited covering surfaces of the complex plane2005

    • Author(s)
      Masaoka, H.
    • Journal Title

      Kodai Math. J 28 no. 2

      Pages: 275-279

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Interpolation of weighted l^q sequences by H^p functions2005

    • Author(s)
      Nakazi, Takahiko
    • Journal Title

      Taiwanese Journal of Mathematics 9 No.3

      Pages: 457-467

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Weighted L^p Sobolev-Lieb-Thirring inequalities2005

    • Author(s)
      Tachizawa, Kazuya
    • Journal Title

      Proc.Japan Acad.Ser.A Math.Sci. 81 no.8

      Pages: 141-143

    • NAID

      120006459413

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Compact perturbations of Hankel Operators2005

    • Author(s)
      Chen, Xiaoman
    • Journal Title

      J.Reine Angew.Math. 51 no.1

      Pages: 1-48

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On a class of closed prime ideals in H^∞2005

    • Author(s)
      Izuchi, Keiji
    • Journal Title

      Complex Variables 50 no.13

      Pages: 1011-1023

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Quasiconformal mappings and minimal Martinboundary of p-sheeted unlimited coveringsurfaces of the complex plane2005

    • Author(s)
      Masaoka, H.
    • Journal Title

      Kodai Math.J. 28 No.2

      Pages: 275-279

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Weighted Sobolev-Lieb-Thirring inequalities2005

    • Author(s)
      Tachizawa, Kazuya
    • Journal Title

      Rev.Mat.Iberoamericana 21

      Pages: 67-85

    • NAID

      120006456909

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Backward shift invariant subspaces in the bidisc2004

    • Author(s)
      Izuchi. Keiji
    • Journal Title

      Hokkaido Math. J. 33no.1

      Pages: 247-254

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Factorizations of functions in H^p(T^n)2004

    • Author(s)
      Nakazi, Takahiko
    • Journal Title

      Complex Variables 49

      Pages: 361-376

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2004 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Backward shift invariant subspaces in the bidisc2004

    • Author(s)
      Izuchi, Keiji
    • Journal Title

      Hokkaido Math. J. 33 no. 1

      Pages: 247-254

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Backward shift invariant subspaces in the bidisc2004

    • Author(s)
      Izuchi, Keiji
    • Journal Title

      Hokkaido Math.J. 33 no.1

      Pages: 247-254

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The role of completeness in the type problem for infinitely sheeted planes2004

    • Author(s)
      Nakai, Mitsuru
    • Journal Title

      Complex Variables 49 no.4

      Pages: 229-240

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Common zero sets of equivalent singular inner functions2004

    • Author(s)
      Izuchi, Keiji
    • Journal Title

      Studia Math. 163 no.3

      Pages: 231-255

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Backward shift invariant subspaces in the bidisc. II2004

    • Author(s)
      Izuchi, Keiji
    • Journal Title

      J.Operator Theory 51 no.2

      Pages: 361-376

    • Related Report
      2004 Annual Research Report
  • [Presentation] Riemann面のRoyden's resolutionとsimultaneous analytic continuation2007

    • Author(s)
      Hayashi, M.
    • Organizer
      関数環研究集会
    • Place of Presentation
      信州大学理学部
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Royden's resolution of a Riemann suface and simultaneous analytic continuation2007

    • Author(s)
      Hayashi. M.
    • Organizer
      Seminar on Funcion Algebras
    • Place of Presentation
      Shinshu Univ
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On a problem about the Shilov boundary of a Riemann surface2006

    • Author(s)
      Hayashi, M.
    • Organizer
      数理解析研究所共同利用研究集会「Analytic Function Spaces and Their Operators」
    • Place of Presentation
      数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] シロフ境界と極値問題の一意性2006

    • Author(s)
      Hayashi, M.
    • Organizer
      関数環研究集会
    • Place of Presentation
      岩手医科大学教養部
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On a problem about the Shilov boundary of a Riemann surface2006

    • Author(s)
      Hayashi. M.
    • Organizer
      RIMS Workshop "Analytic Function Spaces and Their Operators".
    • Place of Presentation
      RIMS
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Shilov boundary and uniquness of linear extremal problem (Japanease)2006

    • Author(s)
      Hayshi. M.
    • Organizer
      Seminar on Function Algebras
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the Shilov boundary of a Riemann surface2005

    • Author(s)
      Hayashi, M.
    • Organizer
      第14回関数空間セミナー(関数環・関数空間の合同シンポジウム)
    • Place of Presentation
      北海道大学理学部
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the Shilov boundary of a Riemann surface2005

    • Author(s)
      Hayashi. M.
    • Organizer
      14th Seminar on Function Spaces (Joint symposium of Function Algebras and Function Spaces).
    • Place of Presentation
      Hokkaido Univ
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary

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Published: 2004-04-01   Modified: 2016-04-21  

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