  We present a theory of general two-point functions and of generalized free
fields in d-dimensional de Sitter space-time which closely parallels the
corresponding minkowskian theory. The usual spectral condition is now replaced
by a certain geodesic spectral condition, equivalent to a precise thermal
characterization of the corresponding ``vacuum''states. Our method is based on
the geometry of the complex de Sitter space-time and on the introduction of a
class of holomorphic functions on this manifold, called perikernels, which
reproduce mutatis mutandis the structural properties of the two-point
correlation functions of the minkowskian quantum field theory. The theory
contains as basic elementary case the linear massive field models in their
``preferred'' representation. The latter are described by the introduction of
de Sitter plane waves in their tube domains which lead to a new integral
representation of the two-point functions and to a Fourier-Laplace type
transformation on the hyperboloid. The Hilbert space structure of these
theories is then analysed by using this transformation. In particular we show
the Reeh-Schlieder property. For general two-point functions, a substitute to
the Wick rotation is defined both in complex space-time and in the complex mass
variable, and substantial results concerning the derivation of Kallen-Lehmann
type representation are obtained.
