Inverse spectral analysis for finite matrix-valued Jacobi operators
| dc.creator | Brüning, Jochen | |
| dc.creator | Chelkak, Dmitry | |
| dc.creator | Korotyaev, Evgeny | |
| dc.date | 2006-07-31 | |
| dc.date.accessioned | 2026-07-07T07:21:12Z | |
| dc.date.available | 2026-07-07T07:21:12Z | |
| dc.description | Consider the Jacobi operators $\cJ$ given by $(\cJ y)_n=a_ny_{n+1}+b_ny_n+a_{n-1}^*y_{n-1}$, $y_n\in \C^m$ (here $y_0=y_{p+1}=0$), where $b_n=b_n^*$ and $a_n:\det a_n\ne 0$ are the sequences of $m\ts m$ matrices, $n=1,..,p$. We study two cases: (i) $a_n=a_n^*>0$; (ii) $a_n$ is a lower triangular matrix with real positive entries on the diagonal (the matrix $\cJ$ is $(2m+1)$-band $mp\ts mp$ matrix with positive entries on the first and the last diagonals). The spectrum of $\cJ$ is a finite sequence of real eigenvalues $ł_1<...<ł_N$, where each eigenvalue $ł_j$ has multiplicity $k_j\le m$. We show that the mapping $(a,b)\mapsto \{(ł_j,k_j)\}_1^N\oplus \{additional spectral data \}$ is 1-to-1 and onto. In both cases (i), \nolinebreak (ii), we give the complete solution of the inverse problem. | |
| dc.identifier | https://arxiv.org/abs/math/0607809 | |
| dc.identifier | http://arxiv.org/abs/math/0607809 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115217 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 47B39 (47A10 81Q10) | |
| dc.title | Inverse spectral analysis for finite matrix-valued Jacobi operators | |
| dc.type | text |