A four dimensional Bernstein Theorem
arXiv:1903.03068 · doi:10.1007/s00009-023-02362-w
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.