Dual Christoffel transformations
Mathematical Physics
2011-08-03 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
Crum's theorem and its modification a la Krein-Adler are formulated for the discrete quantum mechanics with real shifts, whose eigenfunctions consist of orthogonal polynomials of a discrete variable. The modification produces the associated polynomials with a finite number of degrees deleted. This in turn provides the well known Christoffel transformation for the dual orthogonal polynomials with the corresponding positions deleted.
Cite
@article{arxiv.1101.5468,
title = {Dual Christoffel transformations},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:1101.5468},
year = {2011}
}
Comments
41 pages, 4 figures. Comments added. To appear in Prog. Theor. Phys