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Труды Математического института имени В. А. Стеклова, 2006, том 253, страницы 277–295
(Mi tm99)
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Эта публикация цитируется в 13 научных статьях (всего в 13 статьях)
Residual Kernels with Singularities on Coordinate Planes
A. V. Shchupleva, A. K. Tsikha, A. Ygerb a Krasnoyarsk State University
b Université Bordeaux 1
Аннотация:
A finite collection of planes $\{E_\nu \}$ in $\mathbb C^d$ is called an atomic family if the top de Rham cohomology group of its complement is generated by a single element. A closed differential form generating this group is called a residual kernel for the atomic family. We construct new residual kernels in the case when $E_\nu$ are coordinate planes such that the complement $\mathbb C^d\setminus \bigcup E_\nu$ admits a toric action with the orbit space being homeomorphic to a compact projective toric variety. They generalize the well-known Bochner–Martinelli and Sorani differential forms. The kernels obtained are used to establish a new formula of integral representations for functions holomorphic in Reinhardt polyhedra.
Поступило в октябре 2005 г.
Образец цитирования:
A. V. Shchuplev, A. K. Tsikh, A. Yger, “Residual Kernels with Singularities on Coordinate Planes”, Комплексный анализ и приложения, Сборник статей, Труды МИАН, 253, Наука, МАИК «Наука/Интерпериодика», М., 2006, 277–295; Proc. Steklov Inst. Math., 253 (2006), 256–274
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tm99 https://www.mathnet.ru/rus/tm/v253/p277
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