After a short review of the basic properties of analytic functions, we apply the infinite-dimensional theory to get a simple proof of the Cauchy-Kowalevski theorem, in an infinite-dimensional version which seems to be new.
Cite this article
Marc Chaperon, On the Cauchy-Kowalevski Theorem. Enseign. Math. 55 (2009), no. 3, pp. 359–371DOI 10.4171/LEM/55-3-7