Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector-valued reproducing kernel Hilbert $C^*$-modules   The aim of this paper is to present a unified framework in the setting of
Hilbert $C^*$-modules for the scalar- and vector-valued reproducing kernel
Hilbert spaces and $C^*$-valued reproducing kernel spaces. We investigate
conditionally negative definite kernels with values in the $C^*$-algebra of
adjointable operators acting on a Hilbert $C^*$-module. In addition, we show
that there exists a two-sided connection between positive definite kernels and
reproducing kernel Hilbert $C^*$-modules. Furthermore, we explore some
conditions under which a function is in the reproducing kernel module and
present an interpolation theorem. Moreover, we study some basic properties of
the so-called relative reproducing kernel Hilbert $C^*$-modules and give a
characterization of dual modules. Among other things, we prove that every
conditionally negative definite kernel gives us a reproducing kernel Hilbert
$C^*$-module and a certain map. Several examples illustrate our investigation.

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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph