The third Cauchy-Fantappie formula of Leray

Details The third Cauchy-Fantappie formula of Leray The third Cauchy-Fantappie formula of Leray

2002-01-07

arxiv.org/abs/math/0201040v1

Mathematics

Complex Variables

Scientific paper

We study the third Cauchy-Fantappie formula, an integral representation formula for holomorphic functions on a domain in affine space, presented by Jean Leray in the third paper of his famous series "Probleme de Cauchy", published in 1959. We show by means of examples that this formula does not hold without some additional conditions, left unmentioned by Leray. We give sufficient conditions and a necessary condition for the formula to hold, and, in the case of a contractible domain, characterize it cohomologically.

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