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arXiv · 1903.03068

A four dimensional Bernstein Theorem

Alessandro Perotti
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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.

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Alessandro Perotti. 2019-03-07. A four dimensional Bernstein Theorem. https://doi.org/10.1007/s00009-023-02362-w

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