Direct and inverse spectral theory of one-dimensional Schrodinger operators with measures

摘要

We present a direct and rather elementary method for defining and analyzing one-dimensional Schrodinger operators H = -d(2)/dx(2) + mu with measures as potentials. The basic idea is to let the (suitably interpreted) equation -f" + mu f = zf take center stage. We show that the basic results from direct and inverse spectral theory then carry over to Schrodinger operators with measures.