  Positive operator measures (with values in the space of bounded operators on
a Hilbert space) and their generalizations, mainly positive sesquilinear form
measures, are considered with the aim of providing a framework for their
generalized eigenvalue type expansions. Though there are formal similarities
with earlier approaches to special cases of the problem, the paper differs e.g.
from standard rigged Hilbert space constructions and avoids the introduction of
nuclear spaces. The techniques are predominantly measure theoretic and hence
the Hilbert spaces involved are separable. The results range from a Naimark
type dilation result to direct integral representations and a fairly concrete
generalized eigenvalue expansion for unbounded normal operators.
