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Given $t \in \mathbb{R}[0,1]$, consider the following set of polynomials:

$$ \left[-{\left(t - 1\right)}^{2} t, {\left(t - 1\right)} {\left(t^{2} - t - 1\right)}, -{\left(t^{2} - t - 1\right)} t, {\left(t - 1\right)} t^{2}\right]. $$

They show up as the coefficients of an interpolation filter. I've put them in a form that reminds me of Bernstein polynomials. They sum to unity, but don't appear to be orthogonal on $[0,1]$. They might be with respect to some weight function (or other interval).

Other than digging through lists of various types of polynomials, I'm at a loss for terminology to use in searching for further information. Does anyone recognize these as being part of some larger class, regardless of their connection to interpolation?

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    What particular interpolation filter?2012-07-17
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    @J.M. From a cubic convolution kernel. I didn't post too much about the derivation, because I'm interested in the abstract form of the result (i.e. other ways to get there, if any).2012-07-17
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    Something something [cubic spline](https://en.wikipedia.org/wiki/Cubic_Hermite_spline), yes? Apparently a [cardinal spline](https://en.wikipedia.org/wiki/Cubic_Hermite_spline#Cardinal_spline) with tension $c=-1$.2013-01-06
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    Something like that, IIRC.2013-01-07

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