The paper sets up a Riemann-Hilbert problem for matrix Laguerre biorthogonal polynomials from a matrix Pearson equation, derives first- and second-order differential systems, and connects them to eigenvalue problems and matrix discrete Painlevé IV equations.
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math.CA 2years
2019 2verdicts
UNVERDICTED 2representative citing papers
Biorthogonal polynomials are constructed via LU factorization of Gram matrices, recovering Hankel-case properties, classical orthogonal polynomials, and Christoffel-Geronimus perturbation formulas.
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Riemann-Hilbert Problem for the Matrix Laguerre Biorthogonal Polynomials: Eigenvalue Problems and the Matrix Discrete Painlev\'e IV
The paper sets up a Riemann-Hilbert problem for matrix Laguerre biorthogonal polynomials from a matrix Pearson equation, derives first- and second-order differential systems, and connects them to eigenvalue problems and matrix discrete Painlevé IV equations.
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Revisiting Biorthogonal Polynomials. An $LU$ factorization discussion
Biorthogonal polynomials are constructed via LU factorization of Gram matrices, recovering Hankel-case properties, classical orthogonal polynomials, and Christoffel-Geronimus perturbation formulas.