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Zeitschrift für Analysis und ihre Anwendungen


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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.

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