English

An algebra of polyanalytic functions

Complex Variables 2019-05-08 v1

Abstract

The most important uniform algebra is the family of continuous functions on a compact subset KK of the complex plane C\mathbb{C} which are analytic on the interior int(K)(K) For compact sets KK which are regular (i.e. K=K =int(K)(K) and for polyanalytic functions, 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 shall introduce a multiplication on these spaces and investigate the resulting algebras.

Keywords

Cite

@article{arxiv.1905.02514,
  title  = {An algebra of polyanalytic functions},
  author = {Abtin Daghighi and Paul M. Gauthier},
  journal= {arXiv preprint arXiv:1905.02514},
  year   = {2019}
}
R2 v1 2026-06-23T08:59:08.576Z