Inverse problem for the discrete 1D Schrödinger operator with small periodic potentials

Details Inverse problem for the discrete 1D Schrödinger operator with small periodic potentials Inverse problem for the discrete 1D Schrödinger operator with small periodic potentials

2005-07-14

arxiv.org/abs/math/0507297v1

Mathematics

Spectral Theory

will be published in CMP

Scientific paper

Consider the discrete 1D Schr\"odinger operator on $\Z$ with an odd $2k$ periodic potential $q$. For small potentials we show that the mapping: $q\to $ heights of vertical slits on the quasi-momentum domain (similar to the Marchenko-Ostrovski maping for the Hill operator) is a local isomorphism and the isospectral set consists of $2^k$ distinct potentials. Finally, the asymptotics of the spectrum are determined as $q\to 0$.

Affiliated with

Also associated with

No associations

Rating

Inverse problem for the discrete 1D Schrödinger operator with small periodic potentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Inverse problem for the discrete 1D Schrödinger operator with small periodic potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inverse problem for the discrete 1D Schrödinger operator with small periodic potentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-575499