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The Dolbeault complex in infinite dimensions. I. (English) Zbl 0904.32014

The author studies the \(\overline\partial\)-problem, and more generally the Dolbeault complex, on an infinite-dimensional space. This is a fundamental paper, laying foundational work for important future advances. It certain gives vitality to a program that has languished for a great many years.
This is an important contribution to infinite-dimensional analysis.

MSC:

32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
32C81 Applications of analytic spaces to physics and other areas of science
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