Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Inclusion Relation of Reproducing Kernel Hilbert Spaces   To help understand various reproducing kernels used in applied sciences, we
investigate the inclusion relation of two reproducing kernel Hilbert spaces.
Characterizations in terms of feature maps of the corresponding reproducing
kernels are established. A full table of inclusion relations among widely-used
translation invariant kernels is given. Concrete examples for Hilbert-Schmidt
kernels are presented as well. We also discuss the preservation of such a
relation under various operations of reproducing kernels. Finally, we briefly
discuss the special inclusion with a norm equivalence.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org