Journal d’Analyse Mathématique

, Volume 73, Issue 1, pp 165–186 | Cite as

Cauchy integral decomposition for harmonic forms

  • Evsey Dyn’kin


Let ann-dimensional differential form Ω be defined at points of aC 1-smooth boundary π of a domainG ⊂ ℝ n . Under what condition can Ω be represented as Ω = Ω+ + Ω+ + Ω-, where Ω± are forms insideG and outsideG, harmonic in the sense of Hodge? A necessary condition is that both restrictions Ω{inπ and *Ω{inπ be closed in the sense of currents. This condition, with an additional smoothness assumption, turns out to be sufficient as well. This is an analogue of the Cauchy integral decomposition of functions in the plane.


Differential Form Harmonic Form Double Form Lagrange Interpolation Formula Nonvanishing Contribution 
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Copyright information

© Hebrew University of Jerusalem 1997

Authors and Affiliations

  • Evsey Dyn’kin
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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