Abstract
We consider the classical problem of transforming an orthogonality weight of polynomials by means of the space R n . We describe systems of polynomials called pseudo-orthogonal on a finite set of n points. Like orthogonal polynomials, the polynomials of these systems are connected by three-term relations with tridiagonal matrix which is nondecomposable but does not enjoy the Jacobi property. Nevertheless these polynomials possess real roots of multiplicity one; moreover, almost all roots of two neighboring polynomials separate one another. The pseudo-orthogonality weights are partly negative. Another result is the analysis of relations between matrices of two different orthogonal systems which enables us to give explicit conditions for existence of pseudo-orthogonal polynomials.
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Kuznetsov, Y.I. Pseudo-Orthogonal Polynomials. Siberian Mathematical Journal 42, 1093–1101 (2001). https://doi.org/10.1023/A:1012892526816
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DOI: https://doi.org/10.1023/A:1012892526816