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<p>Given a matrix-valued classical pair related to a compact Gelfand pair of rank one, we provide an algorithm to introduce an extra parameter so that the corresponding families of matrix-valued orthogonal polynomials are related by a shift operator (differentiation). We provide a number of examples for which our algorithm is effective. In this way we find new examples and we recover existing examples that have been obtained with another method.</p>

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Matrix-valued Classical Pairs Related to Compact Gelfand Pairs of Rank One: Families and Shift Operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月27日

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  • M. van Pruijssen,
  • P. Román

摘要

Given a matrix-valued classical pair related to a compact Gelfand pair of rank one, we provide an algorithm to introduce an extra parameter so that the corresponding families of matrix-valued orthogonal polynomials are related by a shift operator (differentiation). We provide a number of examples for which our algorithm is effective. In this way we find new examples and we recover existing examples that have been obtained with another method.