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- W2227590129 abstract "In the early nineties, Fokas, Its and Kitaev observed that there is a natural Riemann-Hilbert problem (for 2 x×2 matrix functions) associated with a system of orthogonal polynomials. This Riemann-Hilbert problem was later used by Deift et al. and Bleher and Its to obtain interesting results on orthogonal polynomials, in particular strong asymptotics which hold uniformly in the complex plane. In this paper we will show that a similar Riemann-Hilbert problem (for (r + 1) × (r + 1) matrix functions) is associated with multiple orthogonal polynomials. We show how this helps in understanding the relation between two types of multiple orthogonal polynomials and the higher order recurrence relations for these polynomials. Finally we indicate how an extremal problem for vector potentials is important for the normalization of the Riemann-Hilbert problem. This extremal problem also describes the zero behavior of the multiple orthogonal polynomials." @default.
- W2227590129 created "2016-06-24" @default.
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- W2227590129 date "2001-01-01" @default.
- W2227590129 modified "2023-10-16" @default.
- W2227590129 title "Riemann-Hilbert Problems for Multiple Orthogonal Polynomials" @default.
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- W2227590129 doi "https://doi.org/10.1007/978-94-010-0818-1_2" @default.
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