The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (980 KB) | Metadata | Table of Contents | ZAA summary
Volume 6, Issue 2, 1987, pp. 97–106
DOI: 10.4171/ZAA/233

Published online: 1987-04-30

Lokale Darstellungen differenzierbarer Funktionen auf Banachräumen

N.A. Tu[1]

(1) 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 $p$ a certain $C^2$-function f can be written in the following form: $$f(x) = \alpha (\lambda) + f(p) – \sum^q_{i=1} \alpha_i^2 + \sum^m_{i=q+1} \alpha^2_i$$ 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.

No keywords available for this article.

Tu N.A.: Lokale Darstellungen differenzierbarer Funktionen auf Banachräumen. Z. Anal. Anwend. 6 (1987), 97-106. doi: 10.4171/ZAA/233