Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
An explicit bound for the Łojasiewicz exponent of real polynomials
Tien Son Pham
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2012 年 35 巻 2 号 p. 311-319

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Let f : RnR be a polynomial function of degree d with f(0) = 0. The classical Łojasiewiz inequality states that there exist c > 0 and α > 0 such that |f(x)| ≥ cd(x, f–1(0))α in a neighbourhod of the origin 0 ∈ Rn, where d(x, f–1 (0)) denotes the distance from x to the set f–1(0). We prove that the smallest such exponent α is not greater than R(n, d) with R(n, d) := max{d(3d – 4)n–1, 2d(3d – 3)n–2}.
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© 2012 Department of Mathematics, Tokyo Institute of Technology
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