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Results tagged with several-complex-variables
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user 297
8
votes
Accepted
Computing Dolbeault cohomology of some simple domains
$\def\CC{\mathbb{C}}\def\cO{\mathcal{O}}$Here is a computation of the Dobault cohomology of $X:=B(\infty) \setminus B(0) = \CC^2 \setminus \{ (0,0) \}$. I think that balls of finite radius should be b …
- 156k
9
votes
Accepted
Can all $L^2$ holomorphic functions on a domain vanish at a particular point?
$\def\CC{\mathbb{C}}$Here is a less trivial example that I think works. Let $U \subset \CC^2$ be
$$\{ (x,y) : |x| \leq \min(1, 1/|y|) \}$$
There are lots of $L^2$ holomorphic functions because the ch …
- 156k