  We consider transfer functions of time--invariant systems as defined by
Basseville, Benveniste, Nikoukhah and Willsky when the discrete time is
replaced by the nodes of an homogeneous tree. The complex numbers are now
replaced by a C*-algebra built from the structure of the tree. We define a
point evaluation with values in this C*-algebra and a corresponding ``Hardy
space'' in which a Cauchy's formula holds. This point evaluation is used to
define in this context the counterpart of classical notions such as Blaschke
factors. There are deep analogies with the non stationary setting as developed
by the first author, Dewilde and Dym.

Operator Algebras;Functional Analysis