Various characterisations of extended Chebyshev spaces via blossoms
Let \({\mathcal U}\) be an \(n\)-dimensional space of \({C^{n-1}}\) functions \({(n\geq 1)}\) defined on an interval \(I\). Let \({\mathcal E}\) be the space obtained by integration, namely \[ {\mathcal E}:=\{U\in C^{n}(I) \mid U'\in {\mathcal U}\}. \] The author shows that \({\mathcal U}\) is an extended Chebyshev space if and only if \({\mathcal E}\) possesses some properties given in terms of spaces with nonvanishing Wronskians, Bernstein-like bases, B-spline-like bases, blossoms. The sketch of the proof is given.
scientific article; zbMATH DE number 2136424