Non-Abelian Toda-type equations and matrix valued orthogonal polynomials
Copyright policy )Non-Abelian Toda-type equations and matrix valued orthogonal polynomials
In this paper, we study parameter deformations of matrix valued orthogonal polynomials. These deformations are built on the use of certain matrix valued operators which are symmetric with respect to the matrix valued inner product defined by the orthogonality weight. We show that the recurrence coefficients associated with these operators satisfy generalizations of the non-Abelian lattice equations. We provide a Lax pair formulation for these equations, and an example of deformed Hermite-type matrix valued polynomials is discussed in detail.
- Carlos III University Madrid (UC3M) Spain
- National University of Córdoba Argentina
- Carlos III University of Madrid Spain
- Guangdong Technion-Israel Institute of Technology China (People's Republic of)
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, matrix-valued orthogonal polynomials, Toda system, Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions, Lax pair formulation, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Other hypergeometric functions and integrals in several variables, nonabelian lattice equations, Applications of hypergeometric functions, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 37K10, 33C47, 33C45
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, matrix-valued orthogonal polynomials, Toda system, Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions, Lax pair formulation, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Other hypergeometric functions and integrals in several variables, nonabelian lattice equations, Applications of hypergeometric functions, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 37K10, 33C47, 33C45
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