Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Serre duality and H\"ormander's solution of the $\bar \partial $
  -equation   We use duality in the manner of Serre to generalize a theorem of Hedenmalm on
solution of the $\bar \partial $ equation with inverse of the weight in
H\"ormander $\displaystyle L^{2}$ estimates.\

27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph