Residue currents and Bezout identities
著者
書誌事項
Residue currents and Bezout identities
（Progress in mathematics, v. 114）
Birkhäuser, c1993
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
Introduction 1. Residue currents in one dimension. Different approaches 1. Residue attached to a holomorphic function 2. Some other approaches to the residue current 3. Some variants of the classical Pompeiu formula 4. Some applications of Pompeiu's formulas. Local results 5. Some applications of Pompeiu's formulas. Global results References for Chapter 1 2. Integral formulas in several variables 1. Chains and cochains, homology and cohomology 2. Cauchy's formula for test functions 3. Weighted Bochner-Martinelli formulas 4. Weighted Andreotti-Norguet formulas 5. Applications to systems of algebraic equations References for Chapter 2 3. Residue currents and analytic continuation 1. Leray iterated residues 2. Multiplication of principal values and residue currents 3. The Dolbeault complex and the Grothendieck residue 4. Residue currents 5. The local duality theorem References for Chapter 3 4. The Cauchy-Weil formula and its consequences 1. The Cauchy-Weil formula 2. The Grothendieck residue in the discrete case 3. The Grothendieck residue in the algebraic case References for Chapter 4 5. Applications to commutative algebra and harmonic analysis 1. An analytic proof of the algebraic Nullstellensatz 2. The membership problem 3. The Fundamental Principle of L. Ehrenpreis 4. The role of the Mellin transform References for Chapter 5.
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