  In this paper we present a classification of non-symplectic automorphisms of
K3 surfaces whose order is a multiple of seven by describing the topological
type of their fixed locus. In the case of purely non-symplectic automorphisms,
we provide new results for order 14 and alternative proofs for orders 21, 28
and 42, so that we can unify in the same paper the results on these
automorphisms. For each of these orders we also consider not purely
non-symplectic automorphisms and obtain a complete characterization of their
fixed loci. Several results of our paper were obtained independently in a
recent paper by Brandhorst and Hofmann, but the methods used in the two papers
are completely different.
