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# Inverse spectral problems for coupled oscillating systems: reconstruction from three spectra

### Abstract

We study an inverse spectral problem for a compound oscillating system consisting of a singular string and $N$~masses joined by springs. The operator $A$ corresponding to this system acts in $L_2(0,1)\times C^N$ and is composed of a Sturm-Liouville operator in $L_2(0,1)$ with a distributional potential and a Jacobi matrix in~$C^N$ that are coupled in a special way. We solve the problem of reconstructing the system from three spectra--namely, from the spectrum of $A$ and the spectra of its decoupled parts. A complete description of possible spectra is given.

Key words: Inverse spectral problem, Sturm–Liouville equation, Jacobi matrix, three spectra.

### Article Information

 Title Inverse spectral problems for coupled oscillating systems: reconstruction from three spectra Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 110-123 MathSciNet MR2335605 Copyright The Author(s) 2007 (CC BY-SA)

### Authors Information

S. Albeverio
Institut fur Angewandte Mathematik, Universitat Bonn, Wegelerstr. 6, D--53115, Bonn, Germany; SFB 611, Bonn, Germany; BiBoS, Bielefeld, Germany; IZKS; CERFIM, Locarno, Switzerland; and Accademia di Architettura, Mendrisio, Switzerland

R. Hryniv
Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova, Lviv, 79601, Ukraine

Ya. Mykytyuk
Lviv National University, 1 Universytetska, Lviv, 79602, Ukraine

### Citation Example

S. Albeverio, R. Hryniv, and Ya. Mykytyuk, Inverse spectral problems for coupled oscillating systems: reconstruction from three spectra, Methods Funct. Anal. Topology 13 (2007), no. 2, 110-123.

### BibTex

@article {MFAT356,
AUTHOR = {Albeverio, S. and Hryniv, R. and Mykytyuk, Ya.},
TITLE = {Inverse spectral problems for coupled oscillating systems: reconstruction from three spectra},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {2},
PAGES = {110-123},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=356},
}