Dual Christoffel transformations

Details Dual Christoffel transformations Dual Christoffel transformations

2011-01-28

arxiv.org/abs/1101.5468v2

Prog. Theor. Phys. 126 (2011), 1-34

Physics

Mathematical Physics

41 pages, 4 figures. Comments added. To appear in Prog. Theor. Phys

Scientific paper

10.1143/PTP.126.1

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.

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