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.

Full Text

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},
  MRNUMBER = {MR2335605},
       URL = {http://mfat.imath.kiev.ua/article/?id=356},
}