Abstract:
In this paper, using a Bochner-type theorem,
we establish a characterization of strictly positive
definite functions on the topological direct limit
space
$\mathcal D_{_\infty}$
of real diagonal matrices relatively to the action
of the product group
$K_{_\infty}=U_{_\infty}\times
U_{_\infty}$,
where
$U_{_\infty}$
is the infinite dimensional
unitary group.
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