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

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

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

ISBN-10: 082181348X

ISBN-13: 9780821813485

Pub. Date: 04/12/2000

Publisher: American Mathematical Society

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

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Overview

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.

Product Details

ISBN-13:
9780821813485
Publisher:
American Mathematical Society
Publication date:
04/12/2000
Series:
Translations of Mathematical Monographs, #56
Pages:
165
Product dimensions:
7.00(w) x 10.00(h) x 0.50(d)

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