The inverse problem for the Hill operator, a direct approach

摘要

We consider the Hill operator T=-d2/dx2+V(x) on L2(R), where V∈L2(0,1) is an even 1-periodic real potential and ∫10 V(x) dx=0. It is wellknown that the spectrum of T is absolutely continuous and consists of intervals S1, S2, ... such that Sn=[A+n-1, A-n],..., A+n-1