Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operational calculus for Fourier transform on the group $GL(2,R)$   Consider the Fourier transform on the group $GL(2,R)$ of real $2\times
2$-matrices. We show that Fourier-images of polynomial differential operators
on $GL(2,R)$ are differential-difference operators with coefficients
meromorphic in parameters of representations. Expressions for operators contain
shifts in imaginary direction with respect to the integration contour in the
Plancherel formula. We present explicit formulas for images of partial
derivations and multiplications by coordinates.

4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
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The categories of this paper are: nlin
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: eess