Evgeni Korotyaev (Cardiff): 

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Inverse problem for 1D Schrodinger operators with periodic
distributions (AP)

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ABSTRACT: 

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Consider the 1D Schrodinger operator on the real line, where the periodic potential
is a distribution. The spectrum of this operator is purely absolutely continuous and 
consists of intervals separated by gaps. We solve the inverse 
problem (including characterization) both in terms of vertical slits 
on the quasimomentum domain and in terms of gap lengths. 
Furthermore, we obtain a priori two-sided estimates for these maps.