ENGLISH

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

By Lev Abramovich Aĭzenberg , Sh. A. Dautov

Book information

Publisher
American Mathematical Society
Year
1983
ISBN
082184508X, 9780821845080
LCC
QA331
Language
english
Format
PDF
Filesize
2 MB (2566699 bytes)
Series
Translations of Mathematical Monographs 56
Edition
1
Pages
176\176
DPI
600
Orientation
yes
Scanned
yes
Time added
2012-02-04 16:00:00

Description

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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