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



Author: Vigny Gabriel

Source: https://arxiv.org/







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