An inverse problem related to 2-orthogonal polynomials
OPEN MATHEMATICS, cilt.24, sa.1, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 24 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.1515/math-2025-0283
- Dergi Adı: OPEN MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Technology Collection (ProQuest)
- Ankara Üniversitesi Adresli: Evet
Özet
This paper is interested in the analysis of the 2-orthogonality of a monic polynomial sequence { Q n } n >= 0 ${\left\{{Q}_{n} ight\}}_{n\ge 0}$ constructed as a linear combination of a sequence of monic 2-orthogonal polynomials { P n } n >= 0 ${\left\{{P}_{n} ight\}}_{n\ge 0}$ with P n ( x ) + s n P n - 1 ( x ) = Q n ( x ) + t n Q n - 1 ( x ) $${P}_{n}\left(x ight)+{s}_{n}{P}_{n-1}\left(x ight)={Q}_{n}\left(x ight)+{t}_{n}{Q}_{n-1}\left(x ight)$$ where s n , t n is an element of C ${s}_{n},{t}_{n}\in \mathbb{C}$ , s 1 not equal t 1 and s n t n not equal 0 for all n >= 1. Also, we provide the connection between the truncated banded Hessenberg matrices associated with { P n } n >= 0 ${\left\{{P}_{n} ight\}}_{n\ge 0}$ and { Q n } n >= 0 ${\left\{{Q}_{n} ight\}}_{n\ge 0}$ . Moreover, the applicability of the obtained result is illustrated by an example.