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General Christoffel Perturbations for Mixed Multiple Orthogonal Polynomials
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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 $\tau$ determinants.
Forward citations
Cited by 2 Pith papers
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Mixed Multiple Orthogonal Laurent Polynomials on the Unit Circle
A Gauss-Borel factorization of a rectangular moment matrix yields the first systematic framework for mixed multiple orthogonal Laurent polynomials on the unit circle, with Christoffel and Geronimus perturbation formulas.
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General Geronimus Perturbations for Mixed Multiple Orthogonal Polynomials
For mixed multiple orthogonal polynomials, the paper derives Christoffel-type formulas for general Geronimus perturbations and proves that the perturbed orthogonality exists exactly when certain tau-determinants do no...
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