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

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If aT = for some fec k0 , 1 (X,E) with kE{0,1, ... 0 , 1 (X,E). O. Proof. e. TeC~ur(X). -<1 ck+av (U) 0,1 X X= with T= on U. To do this, we choose a C00 function such that 1 in a neighborhood of U and supp X. 9 (ii), we have Xcc T _A:T B'(TCi,t) + B' on U. 11 we get a form g 00 ec~ 1 (U) with on U. 4 (ii), and, by Proposition 1. 10, 29 Hence, the form has the required property. 14. Dolbeault cohomology. Let E be a holomorphic vector bundle over an n-dimensional complex manifold X, and let oss,rsn be two integers.

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.

K 1 ) of integers l~k 1 < ...

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