A Weyl–Titchmarsh type formula for a discrete Schrödinger operator with Wigner–von Neumann potential

Volume 201 / 2010

Jan Janas, Sergey Simonov Studia Mathematica 201 (2010), 167-189 MSC: Primary 47B36; Secondary 34E10. DOI: 10.4064/sm201-2-4

Abstract

We consider a discrete Schrödinger operator $\mathcal J$ with Wigner–von Neumann potential not belonging to $l^2$. We find the asymptotics of orthonormal polynomials associated to $\mathcal J$. We prove a Weyl–Titchmarsh type formula, which relates the spectral density of $\mathcal J$ to a coefficient in the asymptotics of the orthonormal polynomials.

Authors

  • Jan JanasInstytut Matematyczny
    Polskiej Akademii Nauk
    Św. Tomasza 30
    31-027 Kraków, Poland
    e-mail
  • Sergey SimonovDepartment of Mathematical Physics
    Institute of Physics
    St. Petersburg University
    Ul'yanovskaya 1
    St. Petergoff, St. Petersburg, 198904, Russia
    e-mail

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