The Łojasiewicz exponent of an analytic function at an isolated zero

  • Janusz Gwoździewicz

    Pedagogical University of Cracow, Kraków, Poland

Abstract

Let f be a real analytic function defined in a neighborhood of such that . We describe the smallest possible exponents !, #, / for which we have the following estimates: , , for x near zero with . We prove that , . Moreover where . If f is a polynomial then in a small neighborhood of zero.

Cite this article

Janusz Gwoździewicz, The Łojasiewicz exponent of an analytic function at an isolated zero. Comment. Math. Helv. 74 (1999), no. 3, pp. 364–375

DOI 10.1007/S000140050094