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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.
MSC:
34A55 Inverse problems involving ordinary differential equations
34B24 Sturm-Liouville theory
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References:
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