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Title: Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials
Authors: Coussement, Jonathan ×
Kuijlaars, Arno
Van Assche, Walter #
Issue Date: 2002
Publisher: Iop publishing ltd
Series Title: Inverse problems vol:18 issue:3 pages:923-942
Abstract: We introduce a spectral transform for the finite relativistic Toda lattice (RTL) in generalized form. In the nonrelativistic case, Moser constructed a spectral transform from the spectral theory of symmetric Jacobi matrices. Here we use a non-symmetric generalized eigenvalue problem for a pair of bidiagonal matrices (L, M) to define the spectral transform for the RTL. The inverse spectral transform is described in terms of a terminating T-fraction. The generalized eigenvalues are constants of motion and the auxiliary spectral data have explicit time evolution. Using the connection with the theory of Laurent orthogonal polynomials, we study the long-time behaviour of the RTL. As in the case of the Toda lattice the matrix entries have asymptotic limits. We show that L tends to an upper Hessenberg matrix with the generalized eigenvalues sorted on the diagonal, while M tends to the identity matrix.
URI: 
ISSN: 0266-5611
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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