1999 Fiscal Year Annual Research Report

有理型写像の値分布論の研究

Research Project

Project/Area Number	10640149
Research Institution	YAMAGATA UNIVERSITY
Principal Investigator	森正氣山形大学, 理学部, 教授 (80004456)
Co-Investigator(Kenkyū-buntansha)	仲田正躬山形大学, 理学部, 教授 (20007173) 風間英明九州大学, 大学院・数理学研究科, 教授 (10037252) 戸田暢茂名古屋工業大学, 工学部, 教授 (30004295) 佐藤圓治山形大学, 理学部, 教授 (80107177) 河村新蔵山形大学, 理学部, 教授 (50007176)
Keywords	値分布理論 / 有理形写像 / 除外値 / 動標的 / 一意性定理 / 緩増加関数 / ジュリア集合 / カオス力学系
Research Abstract	代表者の森は,本課題である有理型写像の空間とその中での除外値をもつ写像の希少性について研究し、ネヴァンリナ除外値の消去の問題に関し、P^n(C)への任意の超越的有理型写像あるいは、正則曲線を少し変形し、除外超平面や除外超曲面および、有理的動標的に対する除外値を全く持たない写像に変形できることを証明した。また、P^n(C)への有理形写像全体の空間にある距離を導入し、除外値を全く持たない写像が超越的有理型写像の空間で稠密であることも示した。ここでは、定数写像、有理写像および、超越的有理型写像をはっきり識別できる距離を導入することも出来た。分担者の戸田は、2つの超越的有理型関数f,gの一致の定理について研究し、ある条件の下に、4つの緩増加関数aκ(z)に対し、{z\|f(z)=a_κ(z)}={z\|g(z)=a_κ(z)},(κ=1,...,4)ならば、f=gであることを示した。また、P^n(C)への正則曲線とsubgeneralな位置にあるP^n(C)の超平面の集合に対しネヴァンリナの第二基本定理の不等式のより一般的な形を与えた。また、高次元の複素解析の研究の立場から、風間は,小平の∂∂^^--補題が弱一完備ケーラー多様体で成立するかという問題を、複素擬輪環体C^n/Γのコホモロジー的有限型のトロイダル群に対して肯定的に証明した。安達は、C^n上の解析的多面体Ωの正則部分多様体Vが、もし∂Ωと横断的の交わるならば、V上の各有界正則関数fはΩ上の有界正則関数Fに拡張できることを示した。児玉は、ある弱擬凸領域を双正則自己同型群の観点から特徴づけた。すなわち、C^n上の有界領域が一般化された複素楕円体となる(大域的性質)ための条件を、境界の局所的性質および領域の自己同型群の局所的性質で与えた。一方、関数空間や関数解析的研究の観点から、河村は、確率密度関数の反復作用についての収束定理を得た。佐藤は、コンパクトアーベル群上のフーリェマルチプライヤーに関し、関数空間としてのバナッハ代数的構造や作用関数についての研究成果を得た。

Research Products

(15 results)

All Other

All Publications (15 results)

[Publications] ADACHI Kenzo,-ANDERSOON M.-CHO H.: "L^p and H^p extensions of holomorphic functions from subvarieties of analytic polyhedra,"Pacific Journ.Of Math.,. No.189. 201-210 (1999)
[Publications] ADACHI Kenzo,-CHO Hong Rae: "The uniform estimate of the ∂^^- problem on a difference set of two convex domains"Proc. Of the Fifth Intern. Colloq. On Finite or Infinite Dimensional Complex Analysis, Beijing University. Vol.4-1. 1-6 (1998)
[Publications] KANEKO Makoto-SATO Enji: "Notes on transference of continuity from maximal Fourier multiplier operators on R^n to those on T^n"Interdiscip. Inform. Sci.. Vol.4-1. 97-107 (1998)
[Publications] KAZAMA Hideaki: "∂∂ problem on noncompact Kaehler manifolds."Proc.of the Fifth Intern.Colloq.on Finite or Infinite Dimensional Complex Analysis,Beijing University.. 157-159 (1998)
[Publications] KAZAMA Hideaki-TAKAYAMA Shigeharu: "∂∂ problem on weakly 1-complete Kaehler manifolds."Nagoya Math. J.,. Vol.155. 81-94 (1999)
[Publications] KODAMA Akio,: "An application of Webster's CR-invariant metric to a characterization of generalized complex ellipsoids,"Proc.of the Fifth Intern. Colloq. On Finite or Infinite Dimensional Complex Analysis, Beijing University.. 173-176 (1998)
[Publications] KODAMA Akio,: "A characterization of certain weakly pseudoconvex domains,"Tohoku Math.j.,. Vol.51. 55-64 (1999)
[Publications] MORI Seiki,: "Elimination of defects of meromorphic mappings of C^m into P^n(C),"Proc. Of the Fifth Intern. Colloq. On Finite or Infinite Dimensional Complex Analysis, Beijing University.. 239-244 (1998)
[Publications] MORI Seiki,: "Elimination of defects of meromorphic mappings of C^m into P^n(C),"Annales Academie Scientiarum Fennicae, Mathematica. Vol.24. 89-104 (1999)
[Publications] MORI Seiki,: "Elimination of defects of meromorphic mappings by a small deformation,"Proc.of US-Japan Seminar of the Delaware Conference, Recen Developments in complex Analysis, Kluwer Acad. Publ. 247-258 (1999)
[Publications] MORI S: "Elimination of defects of holomorphic curves into P^n(C)for rational moving targets,"Research Reports of the Nevanlinna Theory and its Applications II, Nippon Institute Technology,. No.50. 60-65 (1999)
[Publications] SATO Enji: "Some operators on Lorentz spaces,"Hokkaido Math, J.. No.28. 363-372 (1999)
[Publications] TODA Nobushige-ISHIZAKI Katsuya: "Unicity theorems for meromorphic functions sharing four small functions,"Kodai Math. J.,. No.21. 350-371 (1998)
[Publications] TODA Nobushige: "On the second fundamental inequality for holomorphic curves,"Bulletin of Nagoya Inst. Of Tech.,. No.50. 123-135 (1998)
[Publications] TODA Nobushige: "Uniqueness theorem for meromorphic functions sharing five small meromorphic functions,"Research Reports of the Nevanlinna Theory and its Applications II, Nippon Institute Technology. No.50. 81-87 (1999)

1999 Fiscal Year Annual Research Report

有理型写像の値分布論の研究

Principal Investigator

森 正氣 山形大学, 理学部, 教授 (80004456)

Research Products

[Publications] ADACHI Kenzo,-ANDERSOON M.-CHO H.: "L^p and H^p extensions of holomorphic functions from subvarieties of analytic polyhedra,"Pacific Journ.Of Math.,. No.189. 201-210 (1999)

[Publications] ADACHI Kenzo,-CHO Hong Rae: "The uniform estimate of the ∂^^- problem on a difference set of two convex domains"Proc. Of the Fifth Intern. Colloq. On Finite or Infinite Dimensional Complex Analysis, Beijing University. Vol.4-1. 1-6 (1998)

[Publications] KANEKO Makoto-SATO Enji: "Notes on transference of continuity from maximal Fourier multiplier operators on R^n to those on T^n"Interdiscip. Inform. Sci.. Vol.4-1. 97-107 (1998)

[Publications] KAZAMA Hideaki: "∂∂ problem on noncompact Kaehler manifolds."Proc.of the Fifth Intern.Colloq.on Finite or Infinite Dimensional Complex Analysis,Beijing University.. 157-159 (1998)

[Publications] KAZAMA Hideaki-TAKAYAMA Shigeharu: "∂∂ problem on weakly 1-complete Kaehler manifolds."Nagoya Math. J.,. Vol.155. 81-94 (1999)

[Publications] KODAMA Akio,: "An application of Webster's CR-invariant metric to a characterization of generalized complex ellipsoids,"Proc.of the Fifth Intern. Colloq. On Finite or Infinite Dimensional Complex Analysis, Beijing University.. 173-176 (1998)

[Publications] KODAMA Akio,: "A characterization of certain weakly pseudoconvex domains,"Tohoku Math.j.,. Vol.51. 55-64 (1999)

[Publications] MORI Seiki,: "Elimination of defects of meromorphic mappings of C^m into P^n(C),"Proc. Of the Fifth Intern. Colloq. On Finite or Infinite Dimensional Complex Analysis, Beijing University.. 239-244 (1998)

[Publications] MORI Seiki,: "Elimination of defects of meromorphic mappings of C^m into P^n(C),"Annales Academie Scientiarum Fennicae, Mathematica. Vol.24. 89-104 (1999)

[Publications] MORI Seiki,: "Elimination of defects of meromorphic mappings by a small deformation,"Proc.of US-Japan Seminar of the Delaware Conference, Recen Developments in complex Analysis, Kluwer Acad. Publ. 247-258 (1999)

[Publications] MORI S: "Elimination of defects of holomorphic curves into P^n(C)for rational moving targets,"Research Reports of the Nevanlinna Theory and its Applications II, Nippon Institute Technology,. No.50. 60-65 (1999)

[Publications] SATO Enji: "Some operators on Lorentz spaces,"Hokkaido Math, J.. No.28. 363-372 (1999)

[Publications] TODA Nobushige-ISHIZAKI Katsuya: "Unicity theorems for meromorphic functions sharing four small functions,"Kodai Math. J.,. No.21. 350-371 (1998)

[Publications] TODA Nobushige: "On the second fundamental inequality for holomorphic curves,"Bulletin of Nagoya Inst. Of Tech.,. No.50. 123-135 (1998)

[Publications] TODA Nobushige: "Uniqueness theorem for meromorphic functions sharing five small meromorphic functions,"Research Reports of the Nevanlinna Theory and its Applications II, Nippon Institute Technology. No.50. 81-87 (1999)

森正氣山形大学, 理学部, 教授 (80004456)