Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Power series as Fourier series   An abstract theory of Fourier series in locally convex topological vector
spaces is developed. An analog of Fej\'{e}r's theorem is proved for these
series. The theory is applied to distributional solutions of Cauchy-Riemann
equations to recover basic results of complex analysis. Some classical results
of function theory are also shown to be consequences of the series expansion.

13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio