Title: Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties
Publisher: American Mathematical Society
Publication Date: 2000
Language: English
ISBN 10: 082181348X
ISBN 13: 9780821813485
Binding: Soft cover
Condition: As New

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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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Text: English, Russian (translation)

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