Titlebook: Andreotti-Grauert Theory by Integral Formulas; Gennadi M. Henkin,Jürgen Leiterer Book 1988 Springer Science+Business Media New York 1988 a

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0743-1643 Overview: 978-0-8176-3413-1978-1-4899-6724-4Series ISSN 0743-1643 Series E-ISSN 2296-505X

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https://doi.org/10.1007/978-1-4899-6724-4analysis; Integral; integral equation; mathematics

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Integral Formulas and First Applications,the arguments which lead from the Poincaré .-lemma and the regularity of the ∂̄-operator to the Dolbeault isomorphism and the theorem on smoothing of the .-cohomology. In Sect. 3 we prove a generalization of the Cauchy-Fantappie formula, which will be called the . Cauchy-Fantappie formula. This form

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The Cauchy-Riemann Equation on q-Convex Manifolds, then dim H. (X, E) < ∞ for all r≥n−q, where, in the . q-convex case, even H. (X, E) = 0 for all r≥n−q. Also in Sect. 12, we prove the following supplement to Theorem 11.2: If D is a non-degenerate . q-convex domain in an n-dimensional complex manifold X, and E is a holomorphic vector bundle over X,

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The Cauchy-Riemann Equation on q-Concave Manifolds,r≤q−1 admit uniquely determined continuations along such extensions (for r=0, this is the global Hartogs extension phenomenon for holomorphic functions). Moreover, corresponding results with uniform estimates are obtained. At the end of Sect. 15 we prove the classical Andreotti-Grauert finiteness th

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O. Pongs,R. Bald,V. A. Erdmann,E. Reinwaldthe arguments which lead from the Poincaré .-lemma and the regularity of the ∂̄-operator to the Dolbeault isomorphism and the theorem on smoothing of the .-cohomology. In Sect. 3 we prove a generalization of the Cauchy-Fantappie formula, which will be called the . Cauchy-Fantappie formula. This form

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