**SALOMON OFMAN**

*
Formule de transformation pour les courants-résidus
*

**Pages** 259-279

**Received:** 8 November 1999

**Mathematics Subject Classification (2000):** 32A27 - 32A40

**Abstract**
In this article, we give a "transformation" formula
for the Residue-currents, i.e. we compute the Residue-current 1/(P^{l}_{j=1}(å^{l}_{k=1}
u^{j}_{k} f_{k})^{aj })
(u^{j}_{k}
and a_{j}
are respectively holomorphic functions and natural integers)
with respect
to the Residues-currents of the powers of 1/f_{k}. This is obtained
through the
use of both the construction of Leray's Residues and the theory of
Coleff-Herrera's
Residue-currents. This transformation formula has several applications,
in
particular it is used in [**O2**], in the form of the corollary 4.5, to
generalize to
any dimension the results on the analytic Radon Transformation obtained
in
[**O1**]. In
the first paragraph, we give the properties of the Residue-currents we
need
later.
In the second one, we give an abstract of the classical theory of
cohomological
residues and we generalize a formula of Leray on the division of the
differential
forms, useful for the computations of some integral Transformations. In
the
third
one, we prove a continuity formula for Residue-currents depending of a
parameter
when the differential form is
d-closed (otherwise, it is easy to get counter-examples, cf. remark
II.6 in
[**O1**]). In the last one, we prove the transformation formula (proposition
4.2 and
theorem 4.3).

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