The set of zeroes of an ``almost polynomial'' function

Author:
Y. Yomdin

Journal:
Proc. Amer. Math. Soc. **90** (1984), 538-542

MSC:
Primary 41A65; Secondary 41A10

MathSciNet review:
733402

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Abstract: Let be a smooth function on the unit -dimensional ball, with the -norm, equal to one. We prove that if for some , the norm of the th derivative of is bounded by , then the set of zeroes of is similar to that of a polynomial of degree . In particular, is contained in a countable union of smooth hypersurfaces; "many" straight lines cross in not more than points, and the -volume of is bounded by a constant, depending only on and .

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DOI:
https://doi.org/10.1090/S0002-9939-1984-0733402-5

Article copyright:
© Copyright 1984
American Mathematical Society