Inverse problems, trace formulae for discrete Schrödinger operators

Hiroshi Isozaki; Evgeny Korotyaev

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arXiv · 1103.2193

Inverse problems, trace formulae for discrete Schrödinger operators

Hiroshi Isozaki·Evgeny Korotyaev

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Abstract

We study discrete Schroedinger operators with compactly supported potentials on the square lattice. Constructing spectral representations and representing S-matrices by the generalized eigenfunctions, we show that the potential is uniquely reconstructed from the S-matrix of all energies. We also study the spectral shift function for the trace class potentials, and estimate the discrete spectrum in terms of the moments of the spectral shift function and the potential.

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BibTeX RIS

Hiroshi Isozaki, Evgeny Korotyaev. 2011-09-12. Inverse problems, trace formulae for discrete Schrödinger operators. https://arxiv.org/abs/1103.2193

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