Residue currents and ideals of holomorphic functions

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Residue currents with prescribed annihilator ideals (2005, methodology): “Thus R k = ∂̄|h|2λ ∧ ξ ∧ (∂̄ξ)k− |λ=0 are precisely the currents considered in [1].”
Decomposition of residue currents (2007, background): “This class of currents, which we call hypermeromorphic, includes all residue currents in this paper and the de nition is modeled on the currents that appear in various works as [1], [4] and [17]; the typical example being the Cole -Herrera product.”