General Christoffel Perturbations for Mixed Multiple Orthogonal Polynomials

2024/05/19 by Manuel Mañas, Mañas, Manuel, Miguel Rojas +1 · 1 citation
Mathematics · #33C45 #33C47 #42C05 #47B36 #47B39 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2405.11630

openalex publication_date 2024/05/19 · openalex created_date 2024/05/22 · openalex updated_date 2026/07/28

Abstract

Performing both right and left multiplication operations using general regular matrix polynomials, which need not be monic and may possess leading coefficients of arbitrary rank, on a rectangular matrix of measures associated with mixed multiple orthogonal polynomials, reveals corresponding Christoffel formulas. These formulas express the perturbed mixed multiple orthogonal polynomials in relation to the original ones. Utilizing the divisibility theorem for matrix polynomials, we establish a criterion for the existence of perturbed orthogonality, expressed through the non-cancellation of certain τ determinants.

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• Uvarov Perturbations for Multiple Orthogonal Polynomials of the Mixed Type on the Step-Line

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