Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On holomorphic domination, I   Let $X$ be a separable Banach space and $u{:} X\to\Bbb{R}$ locally upper
bounded. We show that there are a Banach space $Z$ and a holomorphic function
$h{:} X\to Z$ with $u(x)<\|h(x)\|$ for $x\in X$. As a consequence we find that
the sheaf cohomology group $H^q(X,\Cal{O})$ vanishes if $X$ has the bounded
approximation property (i.e., $X$ is a direct summand of a Banach space with a
Schauder basis), $\Cal{O}$ is the sheaf of germs of holomorphic functions on
$X$, and $q\ge1$. As another consequence we prove that if $f$ is a $C^1$-smooth
$\overline\partial$-closed $(0,1)$-form on the space $X=L_1[0,1]$ of summable
functions, then there is a $C^1$-smooth function $u$ on $X$ with
$\overline\partial u=f$ on $X$.

7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
3
The categories of this paper are: physics
16
The categories of this paper are: stat
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom