A Weyl–Titchmarsh type formula for a discrete Schrödinger operator with Wigner–von Neumann potential
Tom 201 / 2010
Studia Mathematica 201 (2010), 167-189
MSC: Primary 47B36; Secondary 34E10.
DOI: 10.4064/sm201-2-4
Streszczenie
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.
