Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decay and Smoothness for Eigenfunctions of Localization Operators   We study decay and smoothness properties for eigenfunctions of compact
localization operators. Operators with symbols a in the wide modulation space
M^{p,\infty} (containing the Lebesgue space L^p), p<\infty, and windows
\f_1,\f_2 in the Schwartz class are known to be compact. We show that their
L^2-eigenfuctions with non-zero eigenvalues are indeed highly compressed onto a
few Gabor atoms. Similarly, for symbols a in the weighted modulation spaces
M^{\infty}_{v_s\otimes 1} (\rdd), s>0 (subspaces of M^{p,\infty}(\rdd), p>2d/s)
the L^2-eigenfunctions of the localization operator are actually Schwartz
functions.
  An important role is played by quasi-Banach Wiener amalgam and modulation
spaces. As a tool, new convolution relations for modulation spaces and
multiplication relations for Wiener amalgam spaces in the quasi-Banach setting
are exhibited.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: chem-ph