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arXiv · 1712.09047

Polynomial functions as splines

David Kazhdan·Tamar Ziegler
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Abstract

Let $V$ be a vector space over a finite field $k$. We give a condition on a subset $A \subset V$ that allows for a local criterion for checking when a function $f:A \to k$ is a restriction of a polynomial function of degree $<m$ on $V$. In particular, we show that high rank hypersurfaces of $V$ of degree $\ge m$ satisfy this condition. In addition we show that the criterion is robust (namely locally testable in the theoretical computer science jargon).

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David Kazhdan, Tamar Ziegler. 2018-12-04. Polynomial functions as splines. https://arxiv.org/abs/1712.09047

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