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Let \(X\) be a Hermitian complex space of pure dimension with only isolated singularities and \(\pi : M\rightarrow X\) a resolution of singularities. Let \(\Omega \subset \subset X\) be a domain with no singularities in the boundary, \(\Omega ^*=\Omega {\setminus }\!{{\mathrm{Sing}}}X\) and \(\Omega '=\pi ^{-1}(\Omega )\) . We relate \(L^2\) -properties of the \(\overline{\partial }\) and the \(\overline{\partial }\) -Neumann operator on \(\Omega ^*\) to properties of the corresponding operators on \(\Omega '\) (where the situation is classically well understood). Outside some middle degrees, there are compact solution operators for the \(\overline{\partial }\) -equation on \(\Omega ^*\) exactly if there are such operators on the resolution \(\Omega '\) , and the \(\overline{\partial }\) -Neumann operator is compact on \(\Omega ^*\) exactly if it is compact on \(\Omega '\) . 相似文献
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Let X be a pure n-dimensional (where n≥2) complex analytic subset in ? N with an isolated singularity at 0. In this paper we express the L 2-(0,q)- $\overline{\partial}$ -cohomology groups for all q with 1≤q≤n of a sufficiently small deleted neighborhood of the singular point in terms of resolution data. We also obtain identifications of the L 2-(0,q)- $\overline{\partial}$ -cohomology groups of the smooth points of X, in terms of resolution data, when X is either compact or an open relatively compact complex analytic subset of a reduced complex space with finitely many isolated singularities. 相似文献
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John Erik Fornæ ss Nils Ø vrelid Sophia Vassiliadou 《Proceedings of the American Mathematical Society》2005,133(8):2377-2386
We obtain some -results for the operator on forms that vanish to high order on the singular set of a complex space.
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We discuss various known generalizations of the classical Hartogs extension theorem on Stein spaces with arbitrary singularities and present an analytic proof based on \(\overline{\partial}\)-methods. 相似文献
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We give necessary and sufficient conditions for totally real sets in Stein manifolds to admit Carleman approximation of class
Ck{\mathcal C^k}, k ≥ 1, by entire functions. 相似文献
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