Geodesic
A Weyl–Titchmarsh type formula for a discrete Schrödinger operator with Wigner–von Neumann potential
Jan Janas1 ; Sergey Simonov2
1Instytut Matematyczny Polskiej Akademii Nauk Św. Tomasza 30 31-027 Kraków, Poland
2Department of Mathematical Physics Institute of Physics St. Petersburg University Ul'yanovskaya 1 St. Petergoff, St. Petersburg, 198904, Russia
Studia Mathematica, Tome 201 (2010) no. 2, pp. 167-189
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm201-2-4
Keywords: consider discrete schr dinger operator mathcal wigner von neumann potential belonging asymptotics orthonormal polynomials associated mathcal prove weyl titchmarsh type formula which relates spectral density mathcal coefficient asymptotics orthonormal polynomials

Jan Janas  1   ; Sergey Simonov  2

1 Instytut Matematyczny Polskiej Akademii Nauk Św. Tomasza 30 31-027 Kraków, Poland
2 Department of Mathematical Physics Institute of Physics St. Petersburg University Ul'yanovskaya 1 St. Petergoff, St. Petersburg, 198904, Russia 
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     title = {A {Weyl{\textendash}Titchmarsh} type formula
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Jan Janas; Sergey Simonov. A Weyl–Titchmarsh type formula
for a discrete Schrödinger operator
with Wigner–von Neumann potential. Studia Mathematica, Tome 201 (2010) no. 2, pp. 167-189. doi: 10.4064/sm201-2-4

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