Łojasiewicz exponents of non-degenerate holomorohic and mixed functions
Łojasiewicz exponents of non-degenerate holomorohic and mixed functions
复制标题
DOI：
10.2996/kmj/1540951257
复制
发表时间：
2017-04
影响因子：
0.6
通讯作者：
M. Oka
中科院分区：
文献类型：
--
作者：
M. Oka
我们考虑了原点具有孤立奇点的非简并全纯函数的Łojasiewicz不等式。我们给出了Łojasiewicz指数的显式估计，其形式略弱于福井的断言。对于一个加权齐次多项式，我们给出了由Brzostowski， Krasinski和Oleksik在一定条件下（Łojasiewicz非简并性）所推测的较好的估计形式。我们还引入了强非退化混合函数的Łojasiewicz不等式，并将其推广到混合函数。
We consider Łojasiewicz inequalities for a non-degenerate holomorphic function with an isolated singularity at the origin. We give an explicit estimation of the Łojasiewicz exponent in a slightly weaker form than the assertion in Fukui.For a weighted homogeneous polynomial, we give a better estimation in the form which is conjectured by Brzostowski, Krasinski and Oleksik under under some condition (the Łojasiewicz non-degeneracy). We also introduce Łojasiewicz inequality for strongly non-degenerate mixed functions and generalize this estimation for mixed functions.