Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Truncation Dimension for Linear Problems on Multivariate Function Spaces   The paper considers linear problems on weighted spaces of multivariate
functions of many variables. The main questions addressed are: When is it
possible to approximate the solution for the original function of very many
variables by the solution for the same function; however with all but the first
$k$ variables set to zero, so that the corresponding error is small? What is
the truncation dimension, i.e., the smallest number $k=k(\varepsilon)$ such
that the corresponding error is bounded by a given error demand $\varepsilon$?
Surprisingly, $k(\varepsilon)$ could be very small even for weights with a
modest speed of convergence to zero.

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph