Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A functional model for the Fourier--Plancherel operator truncated on the
  positive half-axis   The truncated Fourier operator $\mathscr{F}_{\mathbb{R^{+}}}$, $$
(\mathscr{F}_{\mathbb{R^{+}}}x)(t)=\frac{1}{\sqrt{2\pi}}
\int\limits_{\mathbb{R^{+}}}x(\xi)e^{it\xi}\,d\xi\,,\ \ \
t\in{}{\mathbb{R^{+}}}, $$ is studied. The operator
$\mathscr{F}_{\mathbb{R^{+}}}$ is considered as an operator acting in the space
$L^2(\mathbb{R^{+}})$. The functional model for the operator
$\mathscr{F}_{\mathbb{R^{+}}}$ is constructed. This functional model is the
multiplication operator on the appropriate $2\times2$ matrix function acting in
the space $L^2(\mathbb{R^{+}})\oplus{}L^2(\mathbb{R^{+}})$. Using this
functional model, the spectrum of the operator $\mathscr{F}_{\mathbb{R^{+}}}$
is found. The resolvent of the operator $\mathscr{F}_{\mathbb{R^{+}}}$ is
estimated near its spectrum.

27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol