A study on univalent holomorphic mappings on the unit balls

• Project/Area Number: 19540205
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu Sangyo University
• Principal Investigator: HAMADA Hidetaka Kyushu Sangyo University, 工学部, 教授 (30198808)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2007: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 複素解析 / 単葉 / 変換写像 / レブナー微分方程式 / 螺旋型写像 / 国際情報交換 / ルーマニア:カナダ / 星形写像 / 増大度定理 / 被覆定理 / 係数評価 / 漸近的星形写像 / Bohrの定理

Research Abstract

Aがある条件を満たす正方行列であるとき、ユークリッド単位球上で、A漸近的螺旋形正則写像の概念とAパラメーター表現を持つ単葉正則写像の概念が同一であることを示した。また、複素バナッハ空間の単位球上の星形正則写像の様々な部分族に対する精密な増大度定理、被覆定理および係数評価式を与えた。更に、単位円盤上の正則関数に対するBohrの定理を、複素バナッハ空間の有界balanced領域から複素バナッハ空間内の等質単位球への正則写像に拡張した。

Research Products

• [Journal Article] Spirallike mappings and univalent subordination chains in Cn (2008)
  • Author(s): I. Graham, H. Hamada, G. Kohr, M. Kohr
  • Journal Title: Ann. Scuola Norm. Sup. Pisa Cl. Sci.(5) 7 Pages: 717-740
  • Peer Reviewed
• [Journal Article] Parametric representation and asymptotic starlikeness in Cn (2008)
  • Author(s): I. Graham, H. Hamada, G. Kohr, M. Kohr
  • Journal Title: Proc. Amer. Math. Soc. 136
  • Peer Reviewed
• [Journal Article] Sharp growth theorems and coefficient bounds for starlike mappings in several complex variables (2008)
  • Author(s): H. Hamada, T. Honda
  • Journal Title: Chinese Annals of Mathematics Ser.B, 29
  • Peer Reviewed
• [Journal Article] Asymptotically spirallike mappings in several complex variables (2008)
  • Author(s): I. Graham, H. Hamada, G. Kohr, M. Kohr
  • Journal Title: Journal d'Analyse Mathematique 105
  • Peer Reviewed
• [Journal Article] Spirallike mappings and univalent subordination chains in C^n (2008)
  • Author(s): I. Graham, H. Hamada, G. Kohr, M. Kohr
  • Journal Title: Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 7 Pages: 717-740
  • Peer Reviewed
• [Journal Article] Parabolic starlike mappings in several complex variables (2007)
  • Author(s): H. Hamada, T. Honda, G. Kohr
  • Journal Title: Manuscripta Math. 123
  • Peer Reviewed
• [Journal Article] Parabolic starlike mappings in several complex variables (2007)
  • Author(s): H.Hamada, T.Honda and G.Kohr
  • Journal Title: Manuscripta Math 123 Pages: 301-324
  • Peer Reviewed
• [Journal Article] Asymptotically spirallike mappings in several complex variables
  • Author(s): I.Graham, H.Hamada, G.Kohr and M.Kohr
  • Journal Title: Journal d'Analyse Mathematique (未定)(掲載予定)
  • Peer Reviewed
• [Journal Article] parametric representation and asymptotic starlikeness in C^n
  • Author(s): I.Graham, H.Hamada, G.Kohr and M.Kohr
  • Journal Title: Proc.Amer.Math.Soc (未定)(掲載予定)
  • Peer Reviewed
• [Journal Article] Bohr,s theorem for holomorphic mappings with values in homogeneous balls
  • Author(s): H.Hamada, T.Honda and G.Kohr
  • Journal Title: Israel J.Math (未定)(掲載予定)
  • Peer Reviewed
• [Journal Article] Sharp growth theorems and coefficient bounds for starlike mappings in several complex variables
  • Author(s): H.Hamada and T, Honda
  • Journal Title: Chinese Annals of Mathematics, Ser.B (未定)(掲載予定)
  • Peer Reviewed
• [Presentation] Asymptotic starlikeness in several compelx variables (2007)
  • Author(s): 濱田 英隆
  • Organizer: 平成19年度多変数関数論冬セミナー
  • Place of Presentation: 富山大学
  • Year and Date: 2007-12-23
• [Remarks]
  • URL: http://www.ip.kyusan-u.ac.jp/J/kougaku/tb/hamada/kenkyuu.html