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Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation

✍ Scribed by A.I. Aptekarev; A. Branquinho; F. Marcellán

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 853 KB
Volume: 78
Category: Article
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(96)00138-0

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✦ Synopsis

Transformations of the measure of orthogonality for orthogonal polynomials, namely Freud transformations, are considered. Jacobi matrix of the recurrence coefficients of orthogonal polynomials possesses an isospectral deformation under these transformations. Dynamics of the coefficients are described by generalized Toda equations. The classical Toda lattice equations are the simplest special case of dynamics of the coefficients under the Freud transformation of the measure of orthogonality. Also dynamics of Hankel determinants, its minors and other notions corresponding to the orthogonal polynomials are studied.

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