arXiv Open Access 2007

Dirichlet-like space and capacity in complex analysis in several variables

Gabriel Vigny

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Abstrak

For a Kahler manifold X, we study a space of test functions W* which is a complex version of H1. We prove for W* the classical results of the theory of Dirichlet spaces: the functions in W* are defined up to a pluripolar set and the functional capacity associated to W* tests the pluripolar sets. This functional capacity is a Choquet capacity. The space W* is not reflexive and the smooth functions are not dense in it for the strong topology. So the classical tools of potential theory do not apply here. We use instead pluripotential theory and Dirichlet spaces associated to a current.

Topik & Kata Kunci

math.CV math.FA

Penulis (1)

Gabriel Vigny

Format Sitasi

APA MLA BibTeX

Vigny, G. (2007). Dirichlet-like space and capacity in complex analysis in several variables. https://arxiv.org/abs/0705.3164

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Informasi Jurnal

Tahun Terbit: 2007
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓