A characteristic function
ΘT is defined, in terms of multianalytic operators on Fock spaces, for any noncontractive sequence
T
(T1,…,Td) (
d
N or
d=∞) of operators on a Hilbert space
H. It is shown that if
ΘT is bounded, then it is unitarily equivalent to a compression of an orthogonal projection (on Krein spaces). This leads to a generalization of a theorem of Davis and Foiain spaces and Fourier representations for
d-orthogonal shifts are obtained and used to study the geometry of the canonical minimal isometric dilation associated with a sequence
T of operators on a Hilbert space.