NEGATIVE DEGREE q-BERNSTEIN BASES AND THE MULTIRATIONAL q-BLOSSOM
Rocky Mountain Journal of Mathematics, cilt.55, sa.4, ss.1137-1152, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 55 Sayı: 4
- Basım Tarihi: 2025
- Doi Numarası: 10.1216/rmj.2025.55.1137
- Dergi Adı: Rocky Mountain Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Sayfa Sayıları: ss.1137-1152
- Anahtar Kelimeler: divided difference, homogeneous multirational q-blossom, multirational q-blossom, negative degree q-Bernstein bases, q-Marsden identity
- Hacettepe Üniversitesi Adresli: Evet
Özet
We investigate algebraic properties of the negative degree q-Bernstein bases. Our fundamental tool in this investigation is a recently introduced variant of the blossom, the multirational q-blossom, which provides the dual functionals for the negative degree q-Bernstein basis functions. By applying the dual functional property of the multirational q-blossom, we are readily able to generate several fundamental identities involving the negative degree q-Bernstein bases, including a new variant of Marsden’s identity, a partition of unity property, a reparametrization formula, and a formula for representing monomials. We also show how to use the homogeneous variant of the multirational q-blossom to convert between the q-Taylor bases and the negative degree q-Bernstein bases.