  Full Vertex Operator Algebras (full VOA) are extensions of two commuting
Vertex Operator Algebras, introduced to formulate compact two-dimensional
conformal field theory. We define unitarity, polynomial energy bounds and
polynomial spectral density for full VOA. Under these conditions and local
$C_1$-cofiniteness of the simple full VOA, we show that the correlation
functions of quasi-primary fields define tempered distributions and satisfy a
conformal version of the Osterwalder-Schrader axioms, including the linear
growth condition.
  As an example, we show that a family of full extensions of the Heisenberg VOA
satisfies all these assumptions.
