Integral representation with weights II, division and interpolation

Details Integral representation with weights II, division and interpolation Integral representation with weights II, division and interpolation

2005-11-09

arxiv.org/abs/math/0511238v1

Mathematics

Complex Variables

Scientific paper

Let $f$ be a $r\times m$-matrix of holomorphic functions that is generically surjective. We provide explicit integral representation of holomorphic $\psi$ such that $\phi=f\psi$, provided that $\phi$ is holomorphic and annihilates a certain residue current with support on the set where $f$ is not surjective. We also consider formulas for interpolation. As applications we obtain generalizations of various results previously known for the case $r=1$.

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