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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Separation of real algebraic sets and the Łojasiewicz exponent


Authors: Krzysztof Kurdyka and Stanisław Spodzieja
Journal: Proc. Amer. Math. Soc. 142 (2014), 3089-3102
MSC (2010): Primary 32S50, 14B05, 34A26
Published electronically: May 14, 2014
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Abstract: We discuss several aspects of Łojasiewicz inequalities, namely local and global versions, and the relations between the gradient inequality and regular separation of real algebraic sets. We give effective estimates for Łojasiewicz's exponents in the real and complex setting.


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Additional Information

Krzysztof Kurdyka
Affiliation: Laboratoire de Mathematiques (LAMA), Université de Savoie, UMR-5127 de CNRS, 73-376 Le Bourget-du-Lac cedex, France
Email: Krzysztof.Kurdyka@univ-savoie.fr

Stanisław Spodzieja
Affiliation: Faculty of Mathematics and Computer Science, University of Łódź, S. Banacha 22, 90-238 Łódź, Poland
Email: spodziej@math.uni.lodz.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12061-2
PII: S 0002-9939(2014)12061-2
Keywords: {\L}ojasiewicz exponent, {\L}ojasiewicz inequality with gradient, polynomial, polynomial mapping
Received by editor(s): June 11, 2012
Received by editor(s) in revised form: September 14, 2012
Published electronically: May 14, 2014
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.