Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Divergence for System Approximations   In this paper we analyze the approximation of stable linear time-invariant
systems, like the Hilbert transform, by sampling series for bandlimited
functions in the Paley-Wiener space $\mathcal{PW}_{\pi}^{1}$. It is known that
there exist systems and functions such that the approximation process is weakly
divergent, i.e., divergent for certain subsequences. Here we strengthen this
result by proving strong divergence, i.e., divergence for all subsequences.
Further, in case of divergence, we give the divergence speed. We consider
sampling at Nyquist rate as well as oversampling with adaptive choice of the
kernel. Finally, connections between strong divergence and the Banach-Steinhaus
theorem, which is not powerful enough to prove strong divergence, are
discussed.

33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph