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The eigenvalues’ function (EVF) of the family of Sturm-Liouville operators and the inverse problems T. N. Harutyunyan |
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Abstract: We prove that the union of the spectra of the family of operators of Sturm-Liouville operators (generated by potential q and the family of separated boundary conditions) can be presented as a smooth surface, which we call EVF. We give the algorithm of reconstruction of q by EVF and prove that some uniqueness theorems in inverse problems follow from the properties of EVF. We apply EVF to problem of translation eigenvalues. Language: English |
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