Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati
  Equations   An operator Riccati equation from systems theory is considered in the case
that all entries of the associated Hamiltonian are unbounded. Using a certain
dichotomy property of the Hamiltonian and its symmetry with respect to two
different indefinite inner products, we prove the existence of nonnegative and
nonpositive solutions of the Riccati equation. Moreover, conditions for the
boundedness and uniqueness of these solutions are established.

3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys