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

[摘要] 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 miners and other notions corresponding to the orthogonal polynomials are studied.

[发布日期] 1997-02-03

[关键词] orthogonal polynomials;three term recurrence relations;transformations of the measure;isospectral deformation of Jacobi matrix;directed and inverse spectral problem;Toda lattice