On the relation between the full Kostant–Toda lattice and multiple orthogonal polynomials

The correspondence between a high-order non-symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving explicit expressions for the resolvent function and, under some...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011-05, Vol.377 (1), p.228-238
Main Authors: Barrios Rolanía, D., Branquinho, A., Foulquié Moreno, A.
Format: Article
Language:English
Subjects:
Combinatorics. Ordered structures
Differential equations
Exact sciences and technology
Fourier analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Operator theory
Order, lattices, ordered algebraic structures
Orthogonal polynomials
Recurrence relations
Sciences and techniques of general use
Special functions
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:The correspondence between a high-order non-symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving explicit expressions for the resolvent function and, under some conditions, the representation of the vector of functionals, associated with the solution for our integrable systems. The method of investigation is based on the evolutions of the matrical moments.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.10.044