Abstract
In spline spaces with sections in arbitrary extended Chebyshev spaces and with connections defined by arbitrary lower triangular matrices with positive diagonal elements, we prove that existence of B-spline bases is equivalent to existence of blossoms. As is now classical, we construct blossoms with the help of osculating flats. As for B-spline bases, this expression denotes normalized basis consisting of minimally supported functions which are positive on the interior of their supports and which satisfy an additional “end point condition.”
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Mazure, ML. On the Equivalence Between Existence of B-Spline Bases and Existence of Blossoms. Constr Approx 20, 603–624 (2004). https://doi.org/10.1007/s00365-003-0547-0
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DOI: https://doi.org/10.1007/s00365-003-0547-0