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arXiv · 2512.21891

Non-polynomial divided difference and blossoming

Fatma Zürnacı-Yetiş
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Abstract

Two notable examples of dual functionals in approximation theory and computer-aided geometric design are the blossom and the divided difference operator. Both of these dual functionals satisfy a similar set of formulas and identities. Moreover, the divided differences of polynomials can be expressed in terms of the blossom. In this paper, an extended non-polynomial homogeneous blossom for a wide collection of spline spaces, including trigonometric splines, hyperbolic splines, and special M\"{u}ntz spaces of splines, is defined. It is shown that there is a relation between the non-polynomial divided difference and the blossom, which is analogous to the polynomial case.

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Fatma Zürnacı-Yetiş. 2025-12-26. Non-polynomial divided difference and blossoming. https://arxiv.org/abs/2512.21891

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