Dynamics and interpretation of some integrable systems via multiple orthogonal ...

• Author(s): Branquinho, Amílcar ; Barrios Rolania, Dolores ; Foulquie Moreno, Ana Pilar
• Date: 2010
• Persistent ID: http://hdl.handle.net/10773/8427
• Origin: RIA - Repositório Institucional da Universidade de Aveiro
• Subject(s): Orthogonal polynomials; Differential equations; Recurrence relations
• Document Type: Article
• Language: English

Description

High-order non-symmetric difference operators with complex coefficients are considered. The correspondence between dynamics of the coefficients of the operator defined by a Lax pair and its resolvent function is established. The method of investigation is based on the analysis of the moments for the operator. The solution of a discrete dynamical system is studied. We give explicit expressions for the resolvent function and, under some conditions, the representation of the vector of functionals, associated with the solution for the integrable systems.