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nlin.SI2025
Non-commutative multiple bi-orthogonal polynomials: formal approach and integrability
Adam Doliwa
We define the non-commutative multiple bi-orthogonal polynomial systems, which simultaneously generalize the concepts of multiple orthogonality, matrix orthogonal polynomials and o…
nlin.SI2023
Determinantal approach to multiple orthogonal polynomials, and the corresponding integrable equations
Adam Doliwa
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Padé ap…
nlin.SI2023
Hermite-Padé approximation, multiple orthogonal polynomials, and multidimensional Toda equations
Adam Doliwa
We review recent results on the connection between Hermite-Padé approximation problem, multiple orthogonal polynomials, and multidimensional Toda equations in continuous and discre…