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  1. 121 数理科学研究科
  2. Scientific Papers of the College of Arts and Sciences, The University of Tokyo
  3. 38
  1. 0 資料タイプ別
  2. 30 紀要・部局刊行物
  3. Scientific Papers of the College of Arts and Sciences, The University of Tokyo
  4. 38

Continuous Dependence Problem in an Inverse Spectral Problem for Systems of Ordinary Differential Equations of First Order

https://doi.org/10.15083/00040996
https://doi.org/10.15083/00040996
3d584204-d3d7-4f99-97b1-b8c572319f90
名前 / ファイル ライセンス アクション
scp038005.pdf scp038005.pdf (3.0 MB)
Item type 紀要論文 / Departmental Bulletin Paper(1)
公開日 2008-11-19
タイトル
タイトル Continuous Dependence Problem in an Inverse Spectral Problem for Systems of Ordinary Differential Equations of First Order
言語
言語 eng
資源タイプ
資源 http://purl.org/coar/resource_type/c_6501
タイプ departmental bulletin paper
ID登録
ID登録 10.15083/00040996
ID登録タイプ JaLC
著者 Yamamoto, Masahiro

× Yamamoto, Masahiro

WEKO 139881

Yamamoto, Masahiro

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著者所属
著者所属 Department of Mathematics, College of Arts and Sciences, University of Tokyo
抄録
内容記述タイプ Abstract
内容記述 We consider an eigenvalue problem (1)-(2) : (1) $\begin{pmatrix} 0 & 1 \\ 0 & 1 \end{pmatrix} du(x)/dx +P(x)u(x)=\lambda u(x)$ $(0\leqq x\leqq 1 ; u=\begin{pmatrix} u_1 \\ u_2 \end{pmatrix}$. (2) $u_2()+hu_1(0)=0, u_2(1)+Hu_1(1)=0. $ Here $P=\begin{pmatrix} a & b \\ (p_1) & (p_2) \end{pmatrix} \in {C^1[1,1]}^4 : $ : real-valued and h, H are real constants, and λ corresponds to an eigenvalue. We denote the set of eigenvalues of (1)-(2) by ${\lambda _n)P,h,H)}_(n\in Z)$ under an appropriate numbering. For $Q=\begin{pmatrix} a & b \\ (q_1) & (q_2) \end{pmatrix} \in {C^1[0,1]}^4$ and $h, H, H^*, J, J^* \in R\setminus {-1,1} (H\
eq H^*, J\
eq J^*)$, we obtain the following result on continuous dependence of coefficients and boundary conditions upon eigenvalues : If $\delta _0\equiv \sum _n^\infty =_(-\infty )(\mid \lambda _n(Q,h,J)-\lambda _n(P,h,H)\mid + (\mid \lambda _n(Q,h,J^*)-\lambda _n(P,h,H^*)\mid $ is sufficientrly small, then $\parallel Q-P\parallel _{[c^1[0,1]]^4}\leqq +\mid J-H\mid +\mid J^*-H^*\mid \leqq M\delta _0$ for some constant M>0. Moreover we get $\parallel Q-P\parallel _{[c^1[0,1]]^4}\leqq M$ . We show also that for given $\mu _n, \mu _n ^* \in C (n\in Z)$, there exists a unique $(Q,h,J^*)\in {C^1[0,1]}^4 \times (R\setminus {-1,1})^2$ satisfying $\lambda _n(Q, h, J)=\mu _n$ and $\mu _n(Q,h,j^*)=\mu _n^*$ under appropriate assumptions on $\mu _n, \mu _n^*(n\in Z)$ $(e.g. \sum _n^\infty =_(-\infty )(\mid \mu _n - \lambda _n(P,h,H^*)\mid)$ is sufficiently small.). We prove these results by the principle of contraction mappings and, in order to apply the principle, we establish a priori estimates of solutions to some hyperbolic systems and results on perturbation of Riesz bases.
書誌情報 Scientific papers of the College of Arts and Sciences, the University of Tokyo

巻 38, p. 69-130, 発行日 1988
ISSN
収録物識別子タイプ ISSN
収録物識別子 02897520
書誌レコードID
収録物識別子タイプ NCID
収録物識別子 AA10538733
フォーマット
内容記述タイプ Other
内容記述 application/pdf
日本十進分類法
主題Scheme NDC
主題 410
出版者
出版者 The University of Tokyo
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