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

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

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**Example text**

C~r(U). (ii) For each f~c00 (D) such that af is also continuous on D, over U, 'r we have the representation if 1~r~n-1 ( 1. 16) if r=n. Proof. Choose a C00 function X on G:n with supp X c:c: D and X= 1 in U. 4 (i) and the Koppelman formula ( 1. 8). 17. Theorem. Let E be a holomorphic vector bundle over a compact ndimensional complex manifold X. Then there exist linear operators n C~ O

Accordingly we use the notations p~D(x) and PaD*
*

By dt 1 ... d~. By~ 2: £ RN+1 with 47 For every strictly increasing collection K=(k1 , ... ,k1 ) of integers we set O~k 1 < ... : L_ tk s=1 We orient the manifolds ~K s = 1}. 3) Then, for any strictly increasing collection K=(k 1 , ... ,k 1 ) of integers 1~k 1 < ...