Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On L. Schwartz's boundedness condition for kernels   In previous works we analysed conditions for linearization of hermitian
kernels. The conditions on the kernel turned out to be of a type considered
previously by L. Schwartz in the related matter of characterizing the real
space generated by positive definite kernels. The aim of this note is to find
more concrete expressions of the Schwartz type conditions: in the Hamburger
moment problem for Hankel type kernels on the free semigroup, in dilation
theory (Stinespring type dilations and Haagerup decomposability), as well as in
multi-variable holomorphy. Among other things, we prove that any hermitian
holomorphic kernel has a holomorphic linearization, and hence that holomorphic
kernels automatically satisfy L. Schwartz's boundedness condition.

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The categories of this paper are: q-fin
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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: eess
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th