On the gradient of quasi-homogeneous polynomials
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RIS BIB ENDNOTEOn the gradient of quasi-homogeneous polynomials
Data publikacji: 05.06.2012
Universitatis Iagellonicae Acta Mathematica, 2011, Tom 49, s. 45 - 57
https://doi.org/10.4467/20843828AM.12.003.0455Autorzy
On the gradient of quasi-homogeneous polynomials
Let K be the real or the complex field, and let f : Kn → K be a quasi-homogeneous polynomial with weight w := (w1;w2;...,wn) and degree d. Assume that rf(0) = 0. Łojasiewicz well known gradient inequality states that there exists an open neighbourhood U of the origin in Kn and two positive constants c and p < 1 such that for any x → U we have rf(x) > cf(x)p: We prove that if the set K - (f) of points where the Fedoryuk condition fails to hold is nite, then the gradient inequality holds true with p = 1-minj wj/d. It is also shown that if n = 2; then K-(f) is either empty or reduced to {0}.
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Informacje: Universitatis Iagellonicae Acta Mathematica, 2011, Tom 49, s. 45 - 57
Typ artykułu: Oryginalny artykuł naukowy
Tytuły:
On the gradient of quasi-homogeneous polynomials
On the gradient of quasi-homogeneous polynomials
Université Pierre et Marie Curie, Paris, France
Dalat University, Dalat, Vietnam
Publikacja: 05.06.2012
Status artykułu: Otwarte
Licencja: Żadna
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