TY - JOUR
T1 - Pseudoconvex domains in almost complex abstract wiener spaces
AU - Kusuoka, Shigeo
AU - Taniguchi, Setsuo
PY - 1993/10
Y1 - 1993/10
N2 - The ∂-operator on an almost complex abstract Wiener space (B, H, μ, J) is defined by making use of the Malliavin calculus. The authors then study pseudoconvex domains in B, domains where the ∂-equations ∂u = f(hook) are solvable. As an application, they establish an approximation theorem of holomorphic forms and a Dolbeault type theorem. Examples of such domains, obtained through SDE, one also discussed.
AB - The ∂-operator on an almost complex abstract Wiener space (B, H, μ, J) is defined by making use of the Malliavin calculus. The authors then study pseudoconvex domains in B, domains where the ∂-equations ∂u = f(hook) are solvable. As an application, they establish an approximation theorem of holomorphic forms and a Dolbeault type theorem. Examples of such domains, obtained through SDE, one also discussed.
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U2 - 10.1006/jfan.1993.1123
DO - 10.1006/jfan.1993.1123
M3 - Article
AN - SCOPUS:0346563490
SN - 0022-1236
VL - 117
SP - 62
EP - 117
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -