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MULTIPLE ORTHOGONAL POLYNOMIALS ON THE UNIT
"... Abstract. We introduce multiple orthogonal polynomials on the unit circle. We show how this is related to simultaneous rational approximation to Carathéodory functions (two point HermitePadé approximation near 0 and near infinity). We give a RiemannHilbert problem for which the solution is in term ..."
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Abstract. We introduce multiple orthogonal polynomials on the unit circle. We show how this is related to simultaneous rational approximation to Carathéodory functions (two point HermitePadé approximation near 0 and near infinity). We give a RiemannHilbert problem for which the solution
Multiple orthogonal polynomial ensembles
, 2009
"... Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we introduce the notion of a multiple orthogonal polynomial ens ..."
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Cited by 27 (7 self)
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Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we introduce the notion of a multiple orthogonal polynomial
Multiple orthogonal polynomials associated with
, 2001
"... We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the HermitePadé table. We give some properties of these polynomials: differential properties, a Rodrigues type for ..."
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We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the HermitePadé table. We give some properties of these polynomials: differential properties, a Rodrigues type
ALGEBRAIC THEORY OF MULTIPLE ORTHOGONAL POLYNOMIALS
, 2009
"... In this work we present an algebraic theory of multiple orthogonal polynomials. Our departure point is the three term recurrence relation, with matrix coefficients, satisfied by a sequence of vector multiple orthogonal polynomials. We give some characterizations of multiple orthogonal polynomials ..."
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In this work we present an algebraic theory of multiple orthogonal polynomials. Our departure point is the three term recurrence relation, with matrix coefficients, satisfied by a sequence of vector multiple orthogonal polynomials. We give some characterizations of multiple orthogonal polynomials
On Certain Wronskians of Multiple Orthogonal Polynomials
"... Abstract. We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multiindices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep ..."
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Cited by 1 (0 self)
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Abstract. We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multiindices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians
Multiple Orthogonal Polynomials, Irrationality and Transcendence
"... . We explain the notion of multiple orthogonal polynomials (polyorthogonal polynomials), which is closely related to HermitePad'e rational approximation of a system of Markov functions, and give some explicit examples. As an application we show how multiple orthogonal polynomials can be used t ..."
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Cited by 3 (2 self)
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. We explain the notion of multiple orthogonal polynomials (polyorthogonal polynomials), which is closely related to HermitePad'e rational approximation of a system of Markov functions, and give some explicit examples. As an application we show how multiple orthogonal polynomials can be used
Some Discrete Multiple Orthogonal Polynomials
 J. Comput. Appl. Math
, 2001
"... In this paper we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Ha ..."
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Cited by 26 (2 self)
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and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied in [10] [3]. The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula
A ChristoffelDarboux formula for multiple orthogonal polynomials
 J. Approx. Theory
"... Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a ChristoffelDarboux formula for this kernel for general multiple orthogonal polynom ..."
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Cited by 35 (10 self)
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Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a ChristoffelDarboux formula for this kernel for general multiple orthogonal
Assche, Multiple orthogonal polynomials for classical weights
 MR1990569 (2004g:33014) Licensed to Penn St Univ, University Park. Prepared on Fri Jul 5 09:17:03 EDT 2013 for download from IP 130.203.136.75. License
"... Abstract. A new set of special functions, which has a wide range of applications from number theory to integrability of nonlinear dynamical systems, is described. We study multiple orthogonal polynomials with respect to p>1 weights satisfying Pearson’s equation. In particular, we give a classific ..."
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Cited by 55 (4 self)
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Abstract. A new set of special functions, which has a wide range of applications from number theory to integrability of nonlinear dynamical systems, is described. We study multiple orthogonal polynomials with respect to p>1 weights satisfying Pearson’s equation. In particular, we give a
RiemannHilbert problems for multiple orthogonal polynomials
, 2000
"... In the early nineties, Fokas, Its and Kitaev observed that there is a natural RiemannHilbert problem (for 2 2 matrix functions) associated which a system of orthogonal polynomials. This RiemannHilbert problem was later used by Deift et al. and Bleher and Its to obtain interesting results on ortho ..."
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Cited by 60 (26 self)
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on orthogonal polynomials, in particular strong asymptotics which hold uniformly in the complex plane. In this paper we will show that a similar RiemannHilbert problem (for (r + 1) (r + 1) matrix functions) is associated with multiple orthogonal polynomials. We show how this helps in understanding
Results 1  10
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556,454