A point interaction for the discrete Schr\"odinger operator and generalized Chebyshev polynomials
Spectral Theory
2018-01-03 v2 Mathematical Physics
Classical Analysis and ODEs
Functional Analysis
math.MP
Abstract
We consider semi-infinite Jacobi matrices corresponding to a point interaction for the discrete Schr\"odinger 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.
Cite
@article{arxiv.1703.06624,
title = {A point interaction for the discrete Schr\"odinger operator and generalized Chebyshev polynomials},
author = {D. R. Yafaev},
journal= {arXiv preprint arXiv:1703.06624},
year = {2018}
}
Comments
Compared to the previous version 2 appendices are added