NEGATIVE DEGREE q-BERNSTEIN BASES AND THE MULTIRATIONAL q-BLOSSOM

TUNCER O. O., Simeonov P., Goldman R.

Rocky Mountain Journal of Mathematics, vol.55, no.4, pp.1137-1152, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 4
  • Publication Date: 2025
  • Doi Number: 10.1216/rmj.2025.55.1137
  • Journal Name: Rocky Mountain Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1137-1152
  • Keywords: divided difference, homogeneous multirational q-blossom, multirational q-blossom, negative degree q-Bernstein bases, q-Marsden identity
  • Hacettepe University Affiliated: Yes

Abstract

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.