Zeroes of the spectral density of discrete Schroedinger operator with Wigner-von Neumann potential

Details Zeroes of the spectral density of discrete Schroedinger operator with Wigner-von Neumann potential Zeroes of the spectral density of discrete Schroedinger operator with Wigner-von Neumann potential

2012-03-08

arxiv.org/abs/1203.1935v1

Mathematics

Spectral Theory

Scientific paper

We consider a discrete Schroedinger operator whose potential is the sum of a Wigner-von Neumann term and a summable term. The essential spectrum of this operator equals to the interval [-2,2]. Inside this interval, there are two critical points where eigenvalues may be situated. We prove that, generically, the spectral density of the operator has zeroes of the power type at these points.

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