Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Square summability of variations and convergence of the transfer
  operator   In this paper we study the one-sided shift operator on a state space defined
by a finite alphabet. Using a scheme developed by Walters [13], we prove that
the sequence of iterates of the transfer operator converges under square
summability of variations of the g-function, a condition which gave uniqueness
of a g-measure in [7]. We also prove uniqueness of so-called G-measures,
introduced by Brown and Dooley [2], under square summability of variations.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph