Weyl-Titchmarsh type formula for periodic Schroedinger operator with Wigner-von Neumann potential

2011/02/25 by Pavel Kurasov, Kurasov, Pavel, Sergey Simonov +1 · 1 citation
Computer Science · Mathematics · #34B20 #34E10 #34L20 #34L40 #47E05 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP #msc:34B20 #msc:34E10 #msc:34L20 #msc:34L40 #msc:47E05

paper · pdf · doi:10.48550/arxiv.1102.5213

arxiv created 2011/02/25 · openalex publication_date 2011/02/25 · arxiv updated 2011/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Schroedinger operator on the half-line with periodic background potential perturbed by a certain potential of Wigner-von Neumann type is considered. The asymptotics of generalized eigenvectors for the values of the spectral parameter from the upper half-plane and on the absolutely continuous spectrum is established. Weyl-Titchmarsh type formula for this operator is proven.

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

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