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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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