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PreprintCC BY 4.0arXiv

Piñeiro mixed orthogonal polynomials and bidiagonal factorization

  • Amílcar Branquinho
  • Juan E. F. Díaz
  • Ana Foulquié-Moreno
  • Manuel Mañas
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Abstract

We study mixed multiple orthogonal polynomials associated with rank-one matrices of measures and their recurrence relations. On the step line we identify the corresponding banded recurrence matrix through the Gauss--Borel factorization of the moment matrix. Elementary Christoffel transformations lead to a factorization of this recurrence matrix into lower and upper bidiagonal factors. For the mixed Piñeiro system we derive contour-integral and generalized hypergeometric representations and formulas for the recurrence and factorization coefficients.

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Cite

BibTeXRIS
BibTeX
@misc{branquinho2026piñeiro,
  title = {{Piñeiro mixed orthogonal polynomials and bidiagonal factorization}},
  author = {Amílcar Branquinho and Juan E. F. Díaz and Ana Foulquié-Moreno and Manuel Mañas},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07678},
  eprint = {2609.07678},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07678},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Piñeiro mixed orthogonal polynomials and bidiagonal factorization
AU  - Amílcar Branquinho
AU  - Juan E. F. Díaz
AU  - Ana Foulquié-Moreno
AU  - Manuel Mañas
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07678
UR  - https://arxiv.org/abs/2609.07678
AB  - We study mixed multiple orthogonal polynomials associated with rank-one matrices of measures and their recurrence relations. On the step line we identify the corresponding banded recurrence matrix through the Gauss--Borel factorization of the moment matrix. Elementary Christoffel transformations lead to a factorization of this recurrence matrix into lower and upper bidiagonal factors. For the mixed Piñeiro system we derive contour-integral and generalized hypergeometric representations and formulas for the recurrence and factorization coefficients.
ER  -