Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subnormal weighted shifts on directed trees and composition operators in
  $L^2$ spaces with non-densely defined powers   It is shown that for every positive integer $n$ there exists a subnormal
weighted shift on a directed tree (with or without root) whose $n$th power is
densely defined while its $(n+1)$th power is not. As a consequence, for every
positive integer $n$ there exists a non-symmetric subnormal composition
operator $C$ in an $L^2$ space over a $\sigma$-finite measure space such that
$C^n$ is densely defined and $C^{n+1}$ is not.

21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph