## An algebra of polyanalytic functions

### Volume 165 / 2021

Colloquium Mathematicum 165 (2021), 225-240
MSC: 46J15, 30G30, 35G05, 46E25.
DOI: 10.4064/cm8274-9-2020
Published online: 23 December 2020

#### Abstract

The most important uniform algebra is the family of continuous functions on a compact subset $K$ of the complex plane $\mathbb C $ which are analytic on the interior ${\rm int} (K)$. For polyanalytic functions and compact sets $K$ which are *regular* (i.e. $K=\overline {{\rm int} (K)}$), 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.