Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier Theory on the Complex Plane II: Weak Convergence, Classification
  and Factorization of Singularities   The convergence of DP Fourier series which are neither strongly convergent
nor strongly divergent is discussed in terms of the Taylor series of the
corresponding inner analytic functions. These are the cases in which the
maximum disk of convergence of the Taylor series of the inner analytic function
is the open unit disk. An essentially complete classification, in terms of the
singularity structure of the corresponding inner analytic functions, of the
modes of convergence of a large class of DP Fourier series, is established.
Given a weakly convergent Fourier series of a DP real function, it is shown how
to generate from it other expressions involving trigonometric series, that
converge to that same function, but with much better convergence
characteristics. This is done by a procedure of factoring out the singularities
of the corresponding inner analytic function, and works even for divergent
Fourier series. This can be interpreted as a resummation technique, which is
firmly anchored by the underlying analytic structure.

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The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org