  We generalize two integral representation formulae of Nevanlinna to functions
of several variables. We show that for a large class of analytic functions that
have non-negative imaginary part on the upper polyhalfplane there are
representation formulae in terms of densely defined self-adjoint operators on a
Hilbert space. We introduce three types of structured resolvent of a
self-adjoint operator and identify four different types of representation in
terms of these resolvents. We relate the types of representation that a
function admits to its growth at infinity.
