Extended shockwave decomposability related to boundaries of holomorphic 1-chains within ℂℙ2

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Abstract

We consider the notion of meromorphic Whitney multifunction solutions to ffξ = fη, which yields an enhanced version of the Dolbeault Henkin characterization of boundaries of holomorphic 1-chains within C ℙ2. By analyzing the equations describing meromorphic Whitney multifunction solutions to ffξ = fη and by creating some generalizations of certain linear dependence results, we show that a function G may be decomposed into a sum of such solutions, modulo ξ-affine functions and with a selected bound on the degree of such sum, if and only if Gξξ satisfies a finite set of explicitly constructible partial differential equations.

Original languageEnglish (US)
Pages (from-to)1133-1172
Number of pages40
JournalIndiana University Mathematics Journal
Volume57
Issue number3
DOIs
StatePublished - Aug 19 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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