An inverse spectral problem is studied for the non-selfadjoint matrix Sturm–Liouville differential equation on the half-line. We give a formulation of the inverse problem, prove the corresponding uniqueness theorem and provide a constructive procedure for the solution of the inverse problem by the method of spectral mappings. The obtained results are natural generalizations of the classical results in inverse problem theory for scalar Sturm–Liouville operators.
Editor-in-Chief: Kabanikhin, Sergey I.
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An inverse problem for the non-selfadjoint matrix Sturm–Liouville equation on the half-line
1 Fachbereich Mathematik, Universität Duisburg-Essen, D-47048 Duisburg, Germany. Email: freiling@math.uni-duisburg.de
2 Department of Mathematics, Saratov State University, Astrakhanskaya 83, 410026 Saratov, Russia. Email: yurkova@info.sgu.ru
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 15, Issue 8, Pages 785–798, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2007.042, January 2008
Publication History:
- Received:
- 2006-02-23
- Published Online:
- 2008-01-24
Keywords: Matrix Sturm–Liouville operators; inverse spectral problems; Weyl matrix; method of spectral mappings
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