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<p>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 multiple orthogonal polynomials of the mixed type in the step-line, reveals corresponding Christoffel formulas. These formulas express the perturbed multiple orthogonal polynomials of the mixed type 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\tau \)</EquationSource> </InlineEquation> determinants.</p>

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General christoffel perturbations for multiple orthogonal polynomials of the mixed type on the step-line

  • 期刊论文

  • 发表日期：

    2025年11月10日

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  • Manuel Mañas,
  • Miguel Rojas

摘要

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 multiple orthogonal polynomials of the mixed type in the step-line, reveals corresponding Christoffel formulas. These formulas express the perturbed multiple orthogonal polynomials of the mixed type 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.