English

Polyanalytic Besov spaces and approximation by dilatations

Complex Variables 2023-03-16 v1 Functional Analysis

Abstract

Using partial derivatives zf\partial_zf and \olzf\partial_{\ol z}f, we introduce Besov spaces of polyanalytic functions on the unit disk and on the upper half-plane. We then prove that the dilatations of each function in polyanalytic Besov spaces converge to the same function in norm. This opens the way for the norm approximation of functions in polyanalytic Besov spaces by polyanalytic polynomials.

Keywords

Cite

@article{arxiv.2303.08688,
  title  = {Polyanalytic Besov spaces and approximation by dilatations},
  author = {Ali Abkar},
  journal= {arXiv preprint arXiv:2303.08688},
  year   = {2023}
}
R2 v1 2026-06-28T09:18:41.051Z