Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation order of Kolmogorov diameters via $L^{q}$-spectra and
  applications to polyharmonic operators   We establish a connection between the $L^{q}$-spectrum of a Borel measure
$\nu$ and the approximation order of Kolmogorov diameters in $L_{\nu}^{p}$ in
higher dimensions by extending ideas for the one-dimensional case as developed
by the authors. This leads to improvements of the classical result of Borzov
and Birman/Solomjak for a broad class of singular measures. As an application,
we consider polyharmonic operators and obtain improved upper bounds of the
decay rate of their eigenvalues and show connections to the one-dimensional
Krein-Feller operator.

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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol