Titlebook: Residue Currents and Bezout Identities; Carlos A. Berenstein,Alekos Vidras,Alain Yger Book 1993 Springer Basel AG 1993 algebra.calculus.co

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The Cauchy-Weil Formula and its Consequences,ndieck residue introduced in Chapter 3. We start this section by showing that the Cauchy-Weil formula, at least in some cases, can be derived from the Cauchy formula with weights, proved in Theorem 2.7.

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978-3-0348-9680-1Springer Basel AG 1993

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Residue Currents in one Dimension Different Approaches,Let . be an holomorphic function in a domain . ⊂ ℂ.We assume that . ≢ 0, so that the zero set of . is a discrete subset of .. Let . be a relatively compact subset of . and . ∈ .(.) such that supp(.) ⊂ ., our first goal is to study the expression: . and more precisely what happens if . tends to 0.

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Book 1993back to Euler, is the basis of Ehrenpreis‘s Fundamental Principle for partial differential equations [37;5], [56;5], and has been explicitly stated, for convolution equations, in the work of Berenstein and Taylor [9;5] (we refer to the survey [8;5] for complete references. ) One important point in [

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Carlos A. Berenstein,Alekos Vidras,Roger Gay,Alain Yger