Geodesic
On the structure of residue currents and functionals orthogonal to ideals in the space of holomorphic functions
Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 1083-1102.

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This article investigates residues associated with holomorphic mappings $f=(f_1,\dots,f_p)\colon X\to\mathbb C^p$ defined on a complex space $X$. By means of a new definition of principal value of a residue, it sharpens results of Coleff, Herrera, and Dolbeault concerning the structure of residues. It establishes a connection between residues and functionals in $\mathcal O'(X)$ orthogonal to the ideal $\langle f_1,\dots,f_p\rangle\subset\mathcal O(X)$. Using these results on residues and functionals, a formula is derived for the exponential representation for elements of invariant subspaces and for the solution of homogeneous convolution equations. 
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V. M. Trutnev; A. K. Tsikh. On the structure of residue currents and functionals orthogonal to ideals in the space of holomorphic functions. Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 1083-1102. http://geodesic.mathdoc.fr/item/IM2_1995_59_5_a11/

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