Computation of the Łojasiewicz exponent of nonnegative and nondegenerate analytic functions
2014 ◽
Vol 25
(10)
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pp. 1450092
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Keyword(s):
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 [Formula: see text], is the infimum of the exponents l satisfying the Łojasiewicz inequality. In this paper, we establish a formula for computing the Łojasiewicz exponent [Formula: see text] of f in terms of the Newton polyhedron of f in the case where f is nonnegative and nondegenerate.
2006 ◽
Vol 16
(08)
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pp. 2191-2205
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2021 ◽
Vol 12
(4)
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pp. 16-24
2005 ◽
Vol 28
(1)
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pp. 106-110
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Keyword(s):
2019 ◽
Vol 27
(2)
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pp. 167-177
2004 ◽
Vol 52
(3)
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pp. 231-236
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2000 ◽
Vol 73
(3)
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pp. 257-267
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