arXiv math/05072972005-07-14math.SP

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

Evgeny Korotyaev, Anton Kutsenko

备注：: will be published in CMP
DOI：: 10.1007/s00220-005-1429-z

英文摘要：

Consider the discrete 1D Schrödinger 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 $q\to 0$.

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