English

A four dimensional Bernstein Theorem

Complex Variables 2023-03-15 v1

Abstract

We prove a four dimensional version of the Bernstein Theorem, with complex polynomials being replaced by quaternionic polynomials. We deduce from the theorem a quaternionic Bernstein's inequality and give a formulation of this last result in terms of four-dimensional zonal harmonics and Gegenbauer polynomials.

Keywords

Cite

@article{arxiv.1903.03068,
  title  = {A four dimensional Bernstein Theorem},
  author = {Alessandro Perotti},
  journal= {arXiv preprint arXiv:1903.03068},
  year   = {2023}
}