Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isometries of the product of composition operators on weighted Bergman
  space   In this paper the necessary and sufficient conditions for the product of
composition operators to be isometry are obtained on weighted Bergman space.
With the help of a counter example we also proved that unlike on
$\mathcal{H}^2(\mathbb{D})$ and $\mathcal{A}_{\alpha}^2(\mathbb{D}),$ the
composition operator on $\mathcal{S}^2(\mathbb{D})$ induced by an analytic self
map on $\mathbb{D}$ with fixed origin need not be of norm one. We have
generalized the Schwartz's well known result on
$\mathcal{A}_{\alpha}^2(\mathbb{D})$ which characterizes the almost
multiplicative operator on $\mathcal{H}^2(\mathbb{D}).$

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin