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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Jet-detectable extrema

Author: Angelo Barone Netto
Journal: Proc. Amer. Math. Soc. 92 (1984), 604-608
MSC: Primary 58C27
MathSciNet review: 760952
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Abstract: Given a real polynomial $ f$ with $ f(0) = 0$, we define a finite family of germs of smooth one-variable functions that can be used to test if $ f$ has an extreme value at 0. A generalization is obtained for functions that have $ k$-jets in a suitable sense.

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  • [G] C. Gibson et al., Construction of canonical stratifications--topological stability of smooth mappings, Lecture Notes in Math., vol. 552, Springer-Verlag, Berlin, Heidelberg and New York, 1976.
  • [M] John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0239612

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Article copyright: © Copyright 1984 American Mathematical Society