Lokale Darstellungen differenzierbarer Funktionen auf Banachräumen

Abstract

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

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