Lokale Darstellungen differenzierbarer Funktionen auf Banachräumen

  • N.A. Tu

    Akademie der Landwirtschaftswissenschaften, Berlin, Germany


Local topological properties of differentiable functions on Banach spaces are studied. It will be shown that in the neighborhood of a nondegenerate critial point pp a certain C2C^2-function f can be written in the following form:

f(x)=α(λ)+f(p)i=1qαi2+i=q+1mαi2f(x) = \alpha (\lambda) + f(p) – \sum^q_{i=1} \alpha_i^2 + \sum^m_{i=q+1} \alpha^2_i

where mm is the dimension of some mm-dimensional subspace, the real numbers α1,,αm\alpha_1, \dots, \alpha_m are determined by a basis of this subspace and α(λ\alpha (\lambda) is given by a function λ\lambda. The dimension mm can tend to \infty, while the number qq does not change.

Cite this article

N.A. Tu, Lokale Darstellungen differenzierbarer Funktionen auf Banachräumen. Z. Anal. Anwend. 6 (1987), no. 2, pp. 97–106

DOI 10.4171/ZAA/233