Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beurling's Theorem for Valuation Hilbert Modules and Several Complex
  Variables   We develop a theory of Valuation Hilbert Modules and prove a version of
Beurling's theorem for these. Then we apply our version of Beurling's theorem
to obtain complete descriptions of the closed invariant subspaces of a number
of Hilbert spaces of analytic functions in several complex variables, including
$H^2$ of the polydisk the ball, and bounded symmetric domains, and weighted
$A^2$ spaces on complex analytic manifolds.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph