New PDF release: Andreotti-Grauert Theory by Integral Formulas

By Prof. Dr. Gennadi M. Henkin, Prof. Dr. Jürgen Leiterer (auth.)

ISBN-10: 0817634134

ISBN-13: 9780817634131

ISBN-10: 1489967249

ISBN-13: 9781489967244

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Extra resources for Andreotti-Grauert Theory by Integral Formulas

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6. Proposition. Let D ~ Cn be a domain with piecewise almost c1 boundary, Y=(Y 1 , ... ,YN) a frame forD, v a Leray map for (D,Y), and K=(k 1 , ... ,k 1 ) a strictly increasing collection of integers 1~k 1 < ...

6) for r=O, ... , n-1. 5. Proposition. Let D cc Cn be a domain with almost c1 boundary, and let v be a Leray map for D. 9) 1~r~n-1 (x,thaDx[O, 1] and Rvf = 0 if r=O or r=n. Proof. 5. 6. The operators Tv. 7. Theorem (Cauchy-Fantappie formula for functions). Let D cc ~be a domain with almost c1 boundary, and let v be a Leray map for D. Then, for any continuous complex-valued function f on D such that is also continuous on D, we have the representation at on D. 10) ~In Sect. 11. 7 is given, for instance, in Sect.

Let X be ann-dimensional complex manifold, and 1~q~n an integer. A real-valued c2 function g defined on X will be called q-convex on X if for all xEX. 4 in [H/L]). Remarks to this definition. ~ Clearly, each q-convex function is r-convex for all 1~r~q. 3. 3, because, by this definition, a real-valued c2 function~ is q-convex in a point x with d~(X)fO if and only if there exist local holomorphic coordinates z 1 , ... ,znin a neighborhood of x such that~ is linearly convex with respect to z 1 , ...

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Andreotti-Grauert Theory by Integral Formulas by Prof. Dr. Gennadi M. Henkin, Prof. Dr. Jürgen Leiterer (auth.)

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