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

Authors

  • Ya. V. Mykytyuk 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. O. Hryniv Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova, Lviv, 79601, Ukraine
  • S. Albeverio Lviv National University, 1 Universytetska, Lviv, 79602, Ukraine

DOI:

Keywords:

Inverse spectral problem, Sturm–Liouville equation, Jacobi matrix, 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.

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Published

2007-06-25

Issue

Vol. 13 No. 2 (2007)

Section

Articles

How to Cite

Mykytyuk, Ya. V., et al. “Inverse Spectral Problems for Coupled Oscillating Systems: Reconstruction from Three Spectra”. Methods of Functional Analysis and Topology, vol. 13, no. 2, June 2007, pp. 110-23, https://zen.imath.kiev.ua/index.php/mfat/article/view/343.