  The aim of the paper is to create a link between the theory of reproducing
kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a
group or of a groupoid. More specifically, it is demonstrated on one hand, how
to construct a positive definite kernel and an RKHS for a given unitary
representation of a group(oid), and on the other hand how to retrieve the
unitary representation of a group or a groupoid from a positive definite kernel
defined on that group(oid) with the help of the Moore-Aronszajn theorem. The
kernel constructed from the group(oid) representation is inspired by the kernel
defined in terms of the convolution of functions on a locally compact group.
Several illustrative examples of reproducing kernels related with unitary
representations of groupoids are discussed in detail. The paper is concluded
with the brief overview of the possible applications of the proposed
constructions.
