A convergent approximation scheme for the inverse Sturm-Liouville problem?
نویسنده
چکیده
For the Sturm-Liouville operator L =L,: .VP+ -p” +pv one seeks to reconstruct the coefficient p from knowledge of the sequence of eigen-frequencies (Aj with LJ? =Ajn for some y j # 0). An implementable scheme is: for some N determine pnr so (approximately) pN has minimum norm with eigen-frequencies { A , . . . . .IN/ as given. This is the method ot’ ’generalised interpolation‘ and is shown to give a convergent approximation scheme: p , v i p . The principal technical difficulties are the continuities of the functionals which are shown for p topologised by weak convergence in (HI)’, and the injectivity of p b { i , . : j = 1. 2 .... 1.
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