Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ultimate Generalization to Monotonicity for Uniform Convergence of
  Trigonometric Series   Chaundy and Jolliffe [4] proved that if $\{a_{n}\}$ is a non-increasing
(monotonic) real sequence with $\lim\limits_{n\to \infty}a_{n}=0$, then a
necessary and sufficient condition for the uniform convergence of the series
$\sum_{n=1}^{\infty}a_{n}\sin nx$ is $ \lim\limits_{n\to \infty}na_{n}=0$. We
generalize (or weaken) the monotonic condition on the coefficient sequence
$\{a_{n}\}$ in this classical result to the so-called mean value bounded
variation condition and prove that the generalized condition cannot be weakened
further. We also establish an analogue to the generalized Chaundy and Jolliffe
theorem in the complex space.

15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org