  We derive global analytic representations of fundamental solutions for a
class of linear parabolic systems with full coupling of first order derivative
terms where coefficient may depend on space and time. Pointwise convergence of
the global analytic expansion is proved. This leads to analytic representations
of solutions of initial-boundary problems of first and second type in terms of
convolution integrals or convolution integrals and linear integral equations.
The results have both analytical and numerical impact. Analytically, our
representations of fundamental solutions of coupled parabolic systems may be
used to define generalized stochastic processes. Moreover, some classical
analytical results based on a priori estimates of elliptic equations are a
simple corollary of our main result. Numerically, accurate, stable and
efficient schemes for computation and error estimates in strong norms can be
obtained for a considerable class of Cauchy- and initial-boundary problems of
parabolic type. Furthermore, there are obvious and less obvious applications to
finance and physics. Warning: The argument given in the current version is only
valid in special cases (essentially the scalar case). A more involved argument
is needed for systems and will be communicated soon in a replacement,
