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Title: Ladder operators and differential equations for multiple orthogonal polynomials
Authors: Filipuk, Galina ×
Van Assche, Walter
Zhang, Lun #
Issue Date: May-2013
Publisher: Institute of Physics Publishing
Series Title: Journal of Physics A, Mathematical and Theoretical vol:46 pages:24
Article number: 205204
Abstract: In this paper, we obtain the ladder operators and associated compatibility conditions for the type I and the type II multiple orthogonal polynomials. These ladder equations extend known results for orthogonal polynomials and can be used to derive the differential equations satisfied by multiple orthogonal polynomials. Our approach is based on Riemann-Hilbert problems and the Christoffel-Darboux formula for multiple orthogonal polynomials, and the nearest-neighbor recurrence relations. As an illustration, we give several explicit examples involving multiple Hermite and Laguerre polynomials, and multiple orthogonal polynomials with exponential weights and cubic potentials.
ISSN: 1751-8113
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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