Residue Currents

Tsikh, A. K.; Yger, Alain

doi:10.1023/b:joth.0000020710.57247.b7

Cited by 19 publications

(16 citation statements)

References 57 publications

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“…Cauchy-Weil's integral representation formula (originally introduced in [19]) plays a major role in this paper. Let us briefly recall it in the particular simple case where it happens to be the most useful (one refers for example to [2,8,13,10,18] for a more detailed as well as a presentation in its generality in the analytic or algebraic context). Let f 1 , ..., f n be n holomorphic functions in a bounded open set U ⊂ C n (possibly not connected) and continuous up to ∂U , with no common zero on ∂U , such that additionally there exists a matrix…”

Section: Cauchy-weil's Integral Representation Formula and Lagrange Imentioning

confidence: 99%

About a Non-Standard Interpolation Problem

Alpay

Yger

2018

Comput. Methods Funct. Theory

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Section: Cauchy-weil's Integral Representation Formula and Lagrange Imentioning

confidence: 99%

About a Non-Standard Interpolation Problem

Alpay

Yger

2018

Comput. Methods Funct. Theory

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“…In the multidimensional residue theory, one of the main problems is computing integrals of a closed differential form ω on a complex manifold X that has singularities on a set

T \subset X

over a cycle Γ in

X ∖ T

, see and [, Sect. 13].…”

Section: Introductionmentioning

confidence: 99%

Toric cycles in the complement to a complex curve in (C×)2

Lushin

Pochekutov

2019

Mathematische Nachrichten

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The amoeba of a complex curve in the 2‐dimensional complex torus is its image under the projection onto the real parts of the logarithmic coordinates. A toric cycle in the complement to a curve is a fiber of this projection over a point in the complement to the amoeba of the curve. We consider amoebas of complex algebraic curves defined by so‐called Harnack polynomials. We prove that toric cycles are homologically independent in the complement to a such curve.

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“…The Coleff-Herrera product was defined over an analytic space, however, most of the work on residue currents thereafter has focused on the case of holomorphic functions on a complex manifold. The theory of residue currents has various applications, for example to effective versions of division problems etc., see for example [3], [7], [24] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Residue currents associated with weakly holomorphic functions

Lärkäng

2012

Ark. Mat.

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We construct Coleff-Herrera products and Bochner-Martinelli type residue currents associated with a tuple $f$ of weakly holomorphic functions, and show that these currents satisfy basic properties from the (strongly) holomorphic case, as the transformation law, the Poincar\'e-Lelong formula and the equivalence of the Coleff-Herrera product and the Bochner-Martinelli type residue current associated with $f$ when $f$ defines a complete intersection.Comment: 28 pages. Updated with some corrections from the revision process. In particular, corrected and clarified some things in Section 5 and 6 regarding products of weakly holomorphic functions and currents, and the definition of the Bochner-Martinelli type current

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Residue Currents

Cited by 19 publications

References 57 publications

About a Non-Standard Interpolation Problem

About a Non-Standard Interpolation Problem

Toric cycles in the complement to a complex curve in (C×)2

Residue currents associated with weakly holomorphic functions

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