Dual Christoffel transformations
arXiv:1101.5468 · doi:10.1143/PTP.126.1
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.
41 pages, 4 figures. Comments added. To appear in Prog. Theor. Phys