TY - JOUR
T1 - Polynomial functions as splines
AU - Kazhdan, David
AU - Ziegler, Tamar
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=85064153801&partnerID=8YFLogxK
U2 - 10.1007/s00029-019-0476-9
DO - 10.1007/s00029-019-0476-9
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AN - SCOPUS:85064153801
SN - 1022-1824
VL - 25
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 2
M1 - 31
ER -