THE INVERSE PROBLEM FOR A DISCRETE PERIODIC SCHRODINGER OPERATOR

摘要

We study isospectral sets for a discrete 1D Schroedinger operator on Z with an (N + 1)-periodic potential. We show that for small odd potentials, the isospectral set consists of 2~((N + 1)/2) elements, while for large potentials, the isospectral set consists of(N + 1)! elements. Moreover, asymptotics for endpoints of the spectrum of the Schrodinger operator for small (and large) potentials are determined.