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ネバンリンナ理論とその応用

Research Project

Project/Area Number 08640194
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionNagoya Institute of Technology

Principal Investigator

戸田 暢茂  名古屋工業大学, 工学部, 教授 (30004295)

Co-Investigator(Kenkyū-buntansha) 足立 俊明  名古屋工業大学, 工学部, 助教授 (60191855)
中村 美浩  名古屋工業大学, 工学部, 助教授 (50155868)
岩下 弘一  名古屋工業大学, 工学部, 助教授 (30193741)
山本 和広  名古屋工業大学, 工学部, 教授 (30091515)
中井 三留  名古屋工業大学, 工学部, 教授 (10022550)
Project Period (FY) 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1996: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordsネバンリンナ理論 / 複素平面 / 常微分方程式 / 正則曲線
Research Abstract

1.P(z,w,w',・・・,w^<(n)>)を多項式係数のw,w',・・・'w^<(n)>に関する多項式,Q(z,w)を整関数係数のwに関するd次の多項式(d=degP)としたとき,複素平面での常微分方程式(^*)P(z,w,w',・・・,w(^n)=Q(z,w)の整関数解について調べ、次の結果を得た。
定理.方程式(^*)において、Q(z,w)の最高次の係数=α(z)A(z)+β(z),Aが超越的でα≠0,β及び他の係数は多項式かつp(A)<∞(pは階数を表す)とする。このとき、ある正の定数Kに対して集合{z:|A(z)|>K}の成分がN個(1【less than or equal】N<∞)あったら、方程式(^*)の整関数解fは、
(].su.[)
注.(*)の例としては3つのよく知られた方程式がある。
2.f=[f_1,・・・,f_<n+1>]をCからP^n(C)へのlinearly non-degenerateな正則曲線,XをC^<n+1>のgeneral positionにあるベクトルからなる部分集合,T(r,f)をfの特性関数,
(].su.[)
ここにu(z)=max_<1【less than or equal】j【less than or equal】n>|f_j(z)|,としたとき、次の、Cartanの定理の精密化
定理.a_1,・・・,a_q∈X(1【less than or equal】q<∞)としたとき、
(].su.])
ここに、d=♯X(0),X(0)={a=(a_1,・・・,a_<nj>a_<n+1>)∈X:a_<n+1>=0}.

Report

(1 results)
  • 1996 Annual Research Report
  • Research Products

    (11 results)

All Other

All Publications (11 results)

  • [Publications] N.Toda: "On subsets of C^<n+1> in general position" Proc.Japan Acad.,Ser.A. 72. 55-58 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] N.Toda: "On the order of entire solutions of a differential equation" Bull.Nagoya inst.Tech.48. 121-127 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Nakai: "Brelot spaces of Schrodinger equations" J.Math.Soc.Japan. 48. 275-298 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Nakai: "Monotone discontinuity of lattice equations in a quasilinear harmonic space" Kodai Math.J.19. 282-292 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Nakai: "Existence of Dirichlet infinite measures on the Euclidean unit bal" Hirosnima Math.J.26. 605-621 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Nakai,T.Tada: "The reverse triangle ineguality in normed spaces" New Zealand J.Math.25. 181-193 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Nakai,T.Tada: "Picard principle for neqative planar potentials" Math.Ann.307(to appear). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Ishikawa,M.Nakai: "Regular and stable points in Dirichlet problem" Proc.Japan Acad.Ser,A.73(to appaer). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Adachi: "Circles on a quaternionic space from" J.Math.Soc.Japan. 48. 205-227 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Adachi: "Curvature bounds and trajectories for a magnetic fields on a Hadamard surface" Tsukuba J.Math.20. 225-230 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Adachi: "A comparison theorem for magnetic Jacobi fields" Proc.Edinburgh Math.Soc.40(to appaer). (1997)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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