Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sign intermixing for Riesz bases and frames measured in the
  Kantorovich-Rubinstein norm   We measure a sign interlacing phenomenon for Bessel sequences $ (u_{k})$ in $
L^{2}$ spaces in terms of the Kantorovich--Rubinstein mass moving norm $ \Vert
u_{k}\Vert_{KR}$. Our main observation shows that, quantitatively, the rate of
the decreasing $ \Vert u_{k}\Vert_{KR}\longrightarrow 0$ havily depends on S.
Bernstein $ n$-widths of a compact of Lipschitz functions. In particular, it
depends on the dimension of the measure space. We have sharp results on the
worst and the best rate of convergence of Kantorovich--Rubinstein norms of
frames on $d$-dimensional cube. Those rates are sharp.

36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ