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Integral representation with weights II, division and interpolation

Research paper by Mats Andersson

Indexed on: 09 Nov '05Published on: 09 Nov '05Published in: Mathematics - Complex Variables



Abstract

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 $r=1$.