Skip to content
DraconiticResearch
Search Sources API
188,932 studies31 sourcesUpdated 5 min ago
PreprintCC BY 4.0arXiv

Matrix orthogonal polynomials related to diffference operators for L-orthogonal polynomials

  • Erik Koelink
  • Ana Loureiro
  • Pablo Román
Open at sourcePDFDOICite

Abstract

The difference operator J arising from the higher order occurrence for the L-orthogonal polynomials is studied using various families of matrix orthogonal polynomials. The matrix orthogonal polynomials determine the polar decomposition of J and its adjoint J∗ considered as operators on ℓ2(ℕ). The special case of symmetric J leads to the case where the matrix polynomials reduce to diagonal matrix polynomials. The example of the symmetric case with constant coefficients for L=2 is discussed in detail.

Related

  1. Discrete orthogonal polynomials related to Hahn difference operator
    J. F. Mañas-Mañas, J. J. Moreno-Balcázar, M. N. Rebocho +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Identities and congruences involving orthogonal polynomials and Apéry-like numbers
    Zhi-Hong Sun
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. An Exploration of Lacunary Orthogonal Polynomials Associated with the Geronimus Transformation
    Rachel Bailey, Roman Gavrilov
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. A unified approach via Geronimus transformation to various types of orthogonal polynomials
    Maxim Derevyagin, Juan Carlos García Ardila
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsarXiv
  5. Time-and-band limiting for symmetric classical Dunkl orthogonal polynomials
    M. M. Castro, F. A. Grünbaum
    arXivPreprintarXiv licenceFull textAnalysis & PDEsNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{koelink2026matrix,
  title = {{Matrix orthogonal polynomials related to diffference operators for $L$-orthogonal polynomials}},
  author = {Erik Koelink and Ana Loureiro and Pablo Román},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38603},
  eprint = {2610.38603},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38603},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Matrix orthogonal polynomials related to diffference operators for L-orthogonal polynomials
AU  - Erik Koelink
AU  - Ana Loureiro
AU  - Pablo Román
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38603
UR  - https://arxiv.org/abs/2610.38603
AB  - The difference operator J arising from the higher order occurrence for the L-orthogonal polynomials is studied using various families of matrix orthogonal polynomials. The matrix orthogonal polynomials determine the polar decomposition of J and its adjoint J^∗ considered as operators on ℓ^2(ℕ). The special case of symmetric J leads to the case where the matrix polynomials reduce to diagonal matrix polynomials. The example of the symmetric case with constant coefficients for L=2 is discussed in detail.
ER  -