Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials

14 Feb 2017  ·  Genest Vincent X., Tsujimoto Satoshi, Vinet Luc, Zhedanov Alexei ·

Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed... They are found in particular to be also orthogonal on the restrictions either to the odd or to the even points of the complete orthogonality lattice. This is exploited to design very efficient inverse problem algorithms for the reconstruction of persymmetric Jacobi matrices from spectral points. Isospectral deformations of such matrices are also considered. Expressions for the associated polynomials and their weights are obtained in terms of the undeformed entities. read more

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Classical Analysis and ODEs