Matrix Jacobi biorthogonal polynomials via Riemann–Hilbert problem
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We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann–Hilbert problem we can derive first and second order differential-difference relations that these matrix orthogonal polynomials and the second kind functions associated to them verify. For the corresponding matrix recurrence coefficients, non-Abelian extensions of a family of discrete Painlevé d-P I V _{IV} equations are obtained for the three term recurrence relation coefficients.
- University of Aveiro Portugal
- University of Coimbra Portugal
- Institute of Mathematical Sciences Spain
- University of Sousse Tunisia
- Complutense University of Madrid Spain
Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, Integrable difference and lattice equations; integrability tests, 33C45, 33C47, 42C05, 47A56, Riemann-Hilbert problems, Non-Abelian discrete Painlevé IV equation, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Matrix exponential and similar functions of matrices, non-abelian discrete Painlevé IV equation, Riemann–Hilbert problem, Matrix Pearson equations, discrete integrable systems, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Discrete version of topics in analysis, Discrete integrable systems, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, matrix Pearson equations
Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, Integrable difference and lattice equations; integrability tests, 33C45, 33C47, 42C05, 47A56, Riemann-Hilbert problems, Non-Abelian discrete Painlevé IV equation, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Matrix exponential and similar functions of matrices, non-abelian discrete Painlevé IV equation, Riemann–Hilbert problem, Matrix Pearson equations, discrete integrable systems, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Discrete version of topics in analysis, Discrete integrable systems, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, matrix Pearson equations
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