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Computation of the Łojasiewicz exponent of nonnegative and nondegenerate analytic functions.
- Source :
-
International Journal of Mathematics . Sep2014, Vol. 25 Issue 10, p-1. 13p. 1 Graph. - Publication Year :
- 2014
-
Abstract
- Let f : (ℝn, 0) → (ℝ, 0) be a nonconstant analytic function defined in a neighborhood of the origin 0 ∈ ℝn. The classical Łojasiewicz inequality states that there exist positive constants δ, c and l such that |f(x)| ≥ cd(x, f-1(0))l for |x| ≤ δ, where d(x, f-1(0)) denotes the distance from x to the set f-1(0). The Łojasiewicz exponent of f at the origin 0 ∈ ℝn, denoted by , is the infimum of the exponents l satisfying the Łojasiewicz inequality. In this paper, we establish a formula for computing the Łojasiewicz exponent of f in terms of the Newton polyhedron of f in the case where f is nonnegative and nondegenerate. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0129167X
- Volume :
- 25
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- International Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 99321328
- Full Text :
- https://doi.org/10.1142/S0129167X1450092X