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Dual Christoffel transformations. (English) Zbl 1230.81031

Summary: Crum’s theorem and its modification à 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.

MSC:

81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
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