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

2012/03/08 by Sergey Simonov, Sergey V. Simonov, Simonov, Sergey
Computer Science · Mathematics · #34E10 #47B36 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1203.1935

openalex publication_date 2012/03/08 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Zeroes of the spectral density of the periodic Schroedinger operator with Wigner-von Neumann potential
• Weyl-Titchmarsh type formula for periodic Schroedinger operator with Wigner-von Neumann potential

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