Author | Berenstein, Carlos A. author |
---|---|
Title | Residue Currents and Bezout Identities [electronic resource] / by Carlos A. Berenstein, Alekos Vidras, Roger Gay, Alain Yger |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1993 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8560-7 |
Descript | XI, 160 p. online resource |
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 Pompeiuโs formulas. Local results -- 5. Some applications of Pompeiuโs formulas. Global results -- References for Chapter 1 -- 2. Integral Formulas in Several Variables -- 1. Chains and cochains, homology and cohomology -- 2. Cauchyโs 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