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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/10.15083/000409963d584204-d3d7-4f99-97b1-b8c572319f90
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
scp038005.pdf (3.0 MB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 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 |
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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. |
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| 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 |
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| 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 | |||||
