d-Orthogonal polynomials via matrix method

VARMA S., Göçmez E. E., Verde-Star L.

Linear Algebra and Its Applications, cilt.737, ss.1-16, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 737
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.laa.2026.02.010
  • Dergi Adı: Linear Algebra and Its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1-16
  • Anahtar Kelimeler: Classical d-orthogonal polynomials, d-Orthogonal polynomials, Hessenberg matrix, Orthogonal polynomials
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we establish necessary and sufficient matrix conditions for polynomial sequences to be d-orthogonal and classical d-orthogonal. Our approach employs a matrix method developed by Verde-Star [46], which we extend to characterize d-orthogonality. Moreover, as an application of our framework, the 2-orthogonality of linear combinations of consecutive polynomials is examined, illustrating how these matrix conditions can be utilized in practice. An example constructed with the help of the Tchebychev 2-orthogonal polynomials of the second kind is also established.