Residue Currents and Bezout Identities

Carlos A. Berenstein,etc.,Roger Gay (University of Bordeaux, France),Alekos Vidras (Kyoto University, Japan),Alain Yger (University of Bordeaux, France)

Residue Currents and Bezout Identities
Format
Hardback
Publisher
Birkhauser Verlag AG
Country
Switzerland
Published
1 September 1993
Pages
168
ISBN
9783764329457

Residue Currents and Bezout Identities

Carlos A. Berenstein,etc.,Roger Gay (University of Bordeaux, France),Alekos Vidras (Kyoto University, Japan),Alain Yger (University of Bordeaux, France)

The objective of this monograph is to present a coherent picture of the almost mysterious role that analytic methods and, in particular, multidimensional residue have recently played in obtaining effective estimates for problems in commutative algebra. Bezout identifies, i.e.,f1g1+…+fmgm=1, appear naturally in many problems, for example in commutative algebra in the Nullstellensatz, and in signal processing in the deconvolution problem. One way to solve them is by using explicit interpolation formulas in Cn, and these depend on the theory of multidimensional residues. The authors present this theory in detail, in a form developed by them, and illustrate its applications to the effective Nullstellensatz and to the Fundamental Principle for convolution equations.

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