A point interaction for the discrete Schrödinger operator and generalized Chebyshev polynomials

Abstract

We consider semi-infinite Jacobi matrices corresponding to a point interaction for the discrete Schrödinger operator. Our goal is to find explicit expressions for the spectral measure, the resolvent and other spectral characteristics of such Jacobi matrices. It turns out that their spectral analysis leads to a new class of orthogonal polynomials generalizing the classical Chebyshev polynomials.

Compared to the previous version 2 appendices are added

References in corpus (1)

• On the spectrum of discrete Schrödinger equation with one-dimensional perturbation

Cited by in corpus (4)

• Attractors of Hamilton nonlinear partial differential equations
• Global attractor for 1D Dirac field coupled to nonlinear oscillator
• Analytic scattering theory for Jacobi operators and Bernstein-Szegö asymptotics of orthogonal polynomials
• Calculating the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials