Polynomial functions as splines

David Kazhdan*, Tamar Ziegler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let V be a vector space over a finite field k. We give a condition on a subset A⊂ V that allows for a local criterion for checking when a function f: A→ 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 ≥ m satisfy this condition. In addition we show that the criterion is robust (namely locally testable in the theoretical computer science jargon).

Original languageAmerican English
Article number31
JournalSelecta Mathematica, New Series
Volume25
Issue number2
DOIs
StatePublished - 1 Jun 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

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