Potentials on abstract Wiener space

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Abstract

The infinite dimensional Green measure g is shown to be a product measure and this provides sufficient conditions for the existence and the differentiability of potentials. Moreover, it is shown how such conditions can be used to prove that if f is Lip and if we set u = Gf, then first D2u is Lip too and second u satisfies Δu = -2f for a wide class of functions f with arbitrary support.

Original languageEnglish (US)
Pages (from-to)215-231
Number of pages17
JournalJournal of Functional Analysis
Volume26
Issue number3
DOIs
StatePublished - Nov 1977
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

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