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Discontinuous inverse eigenvalue problems. (English) Zbl 0541.34012
The author considers inverse Sturm-Liouville problems in which the eigenfunctions have a discontinuity in an interior point and proves that if the potential is known over half the interval and if one boundary condition is given then the potential and the other boundary condition are uniquely determined by the eigenvalues. The theory is applied to the inverse problem for the Earth and it is shown that if the density is known in the lower mantle and the velocity of the shear waves is given throughout the mantle and in the crust then the density is uniquely determined by the eigenfrequencies of the torsional modes with a fixed angular order.
MSC:
34L99Ordinary differential operators
34A55Inverse problems of ODE