AN ALGEBRA OF POLYANALYTIC FUNCTIONS

The most important uniform algebra is the family of continuous functions on a compact subset K of the complex plane C which are analytic on the interior int(K). For polyanalytic functions and compact sets K which are regular (i.e. K = <(int(K)))over bar, we introduce analogous spaces, which are Banach spaces with respect to the sup-norm, but are not closed with respect to the usual pointwise multiplication. We introduce a multiplication on these spaces and investigate the resulting algebras.