A Jacobi type Christoffel-Darboux formula for multiple orthogonal polynomials of mixed type
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2015
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Elsevier Science
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Abstract
An alternative expression for the Christoffel-Darboux formula for multiple orthogonal polynomials of mixed type is derived from the LU factorization of the moment matrix of a given measure and two sets of weights. We use the action of the generalized Jacobi matrix J, also responsible for the recurrence relations, on the linear forms and their duals to obtain the result.
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©2014 Elsevier Inc. All rights reserved.
GA thanks economical support from the Universidad Complutense de Madrid Program “Ayudas para Becas y Contratos Complutenses Predoctorales en España 2011”. MM thanks economical support from the Spanish “Ministerio de Econom´ıa y Competitividad” research project MTM2012-36732-C03-01, Ortogonalidad y aproximacion; Teoria y Aplicaciones. The authors will like to thank the anonymous work of one the referees, his comments and suggestions have clearly improve the quality of this paper.