Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representing a product system representation as a contractive semigroup
  and applications to regular isometric dilations   In this paper we propose a new technical tool for analyzing representations
of Hilbert $C^*$-product systems. Using this tool, we give a new proof that
every doubly commuting representation over $\mathbb{N}^k$ has a regular
isometric dilation, and we also prove sufficient conditions for the existence
of a regular isometric dilation of representations over more general
subsemigroups of $\mathbb{R}_+^k$.

13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex