Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Bondarenko N. P. The Inverse Problem of Spectral Analysis for the Matrix Sturm – Liouville Equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2010, vol. 10, iss. 4, pp. 3-13. DOI: 10.18500/1816-9791-2010-10-4-3-13

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.11.2010
Full text:
(downloads: 159)
Language: 
Russian
Heading: 
UDC: 
517.984

The Inverse Problem of Spectral Analysis for the Matrix Sturm – Liouville Equation

Autors: 
Bondarenko N. P., Saratov State University
Abstract: 

The inverse spectral problem is investigated for the matrix Sturm - Liouville equation on a finite interval. The article provides properties of spectral characteristics, a constructive procedure for the solution of the inverse problem along with necessary and sufficient conditions for its solvability has been obtained.

References: 
  1. Юрко, В.А. Введение в теорию обратных спектральных задач / В.А. Юрко. – М.: Физматлит, 2007. – 384 с.
  2. Yurko, V.A. Inverse problems for matrix Sturm – Liouville operators / V.A. Yurko // Russian J. of Math. Physics. – 2006. – V. 13, № 1. – P. 111–118.
  3. Carlson, R. An inverse problem for the matrix Schr¨odinger equation / R. Carlson // J. of Math. Analysis and Applications. – 2002. – № 267. – P. 564–575.
  4. Malamud, M.M. Uniqueness of the matrix Sturm – Liouville equation given a part of the monodromy matrix and borg type results / M.M. Malamud // Sturm – Liouville theory. Past and present. – Birkhauser; Basel, 2005. – P. 237–270,
  5. Yurko, V.A. Inverse problems for the matrix Sturm – Liouville equation on a finite interval / V.A. Yurko // Inverse Problems. – 2006. – № 22. – P. 1139–1149.
  6. Chelkak, D. Weyl – Titchmarsh functions of vectorvalued Sturm – Liouville operators on the unit interval / D. Chelkak, E. Korotyaev // J. of Functional Analysis. – 2009. – V. 257, iss. 5, 1 September. – P. 1546–1588.