Inverse problems, trace formulae for discrete Schrödinger operators

Details Inverse problems, trace formulae for discrete Schrödinger operators Inverse problems, trace formulae for discrete Schrödinger operators

2011-03-11

arxiv.org/abs/1103.2193v2

Mathematics

Spectral Theory

Ann. Henri Poincar\'e, 2011

Scientific paper

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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