The third Cauchy-Fantappie formula of Leray
Complex Variables
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0201040,
title = {The third Cauchy-Fantappie formula of Leray},
author = {Cezar Joita and Finnur Larusson},
journal= {arXiv preprint arXiv:math/0201040},
year = {2007}
}