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Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties

✍ Scribed by L. A. Aizenberg, Sh. A. Dautov

Publisher
American Mathematical Society
Year
1983
Tongue
English
Leaves
173
Series
Translations of Mathematical Monographs 56
Edition
1
Category
Library
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✦ Synopsis

The authors consider the problem of characterizing the exterior differential forms which are orthogonal to holomorphic functions (or forms) in a domain $D\subset {\mathbf C}^n$ with respect to integration over the boundary, and some related questions. They give a detailed account of the derivation of the Bochner-Martinelli-Koppelman integral representation of exterior differential forms, which was obtained in 1967 and has already found many important applications. They study the properties of $\overline \partial$-closed forms of type $(p, n - 1), 0\leq p\leq n - 1$, which turn out to be the duals (with respect to the orthogonality mentioned above) to holomorphic functions (or forms) in several complex variables, and resemble holomorphic functions of one complex variable in their properties.

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