Abstract
For polynomial splines as well as for Chebyshev splines, it is known that total positivity of the connection matrices is sufficient to obtain B-spline bases. In this paper we give a necessary and sufficient condition for the existence of B-bases (or, equivalently, of blossoms) for splines with connection matrices and with sections in different four-dimensional extended Chebyshev spaces.
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Mazure, ML. Chebyshev splines beyond total positivity. Advances in Computational Mathematics 14, 129–156 (2001). https://doi.org/10.1023/A:1016616731472
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DOI: https://doi.org/10.1023/A:1016616731472