zbMATH — the first resource for mathematics

Uniqueness of the potential function for the vectorial Sturm-Liouville equation on a finite interval. (English) Zbl 1277.34016
Summary: The vectorial Sturm-Liouville operator \[ L_Q=-\frac{d^2}{dx^2}+Q(x) \] is considered, where \(Q\) is an integrable \(m \times m\) matrix-valued function defined on the interval \([0,\pi]\) The authors prove that \(m^2+1\) characteristic functions can determine the potential function of a vectorial Sturm-Liouville operator uniquely. In particular, if \(Q(x)\) is real symmetric, then \(\frac{m(m+1)}{2}+1\) characteristic functions can determine the potential function uniquely. Moreover, if only the spectral data of self-adjoint problems are considered, then \(m^2 + 1\) spectral data can determine \(Q(x)\) uniquely.
34A55 Inverse problems involving ordinary differential equations
34B24 Sturm-Liouville theory
Full Text: DOI
[1] doi:10.1070/RM1964v019n03ABEH001151 · Zbl 0125.00413
[2] doi:10.1006/jmaa.2001.7792 · Zbl 1003.34011
[3] doi:10.1006/jdeq.1999.3758 · Zbl 0970.34073
[4] doi:10.1002/1522-2616(200206)239:1<103::AID-MANA103>3.0.CO;2-F
[5] doi:10.1023/A:1007498010532 · Zbl 0944.34015
[6] doi:10.1088/0266-5611/16/3/313 · Zbl 0988.34023
[7] doi:10.1088/0266-5611/17/5/303 · Zbl 0996.34021
[8] doi:10.1088/0266-5611/23/6/011 · Zbl 1136.34010
[9] doi:10.1088/0266-5611/22/4/002 · Zbl 1107.34005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.