March 24, 2003
Dan Volok
Title: Point evaluation and Hardy space on a homogeneous tree
We consider the stationary transfer functions as defined by Basseville, Benveniste, Nikoukhah and Willsky, when the discrete time is replaced by the nodes of a 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 Cauchy formula holds. The 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 Alpay, Dewilde and Dym.
This is a joint work with Daniel Alpay.