A Quaternionic Bernstein Theorem

被引：0
|
作者：
Alessandro Perotti
机构：
[1] University of Trento,Department of Mathematics
来源：
Mediterranean Journal of Mathematics | 2023年 / 20卷
关键词：
Bernstein theorem; Bernstein inequality; quaternionic polynomials; zonal harmonics; Primary 30G35; Secondary 26D05; 33C50;
D O I：
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中图分类号：
学科分类号：
摘要：
We prove a four-dimensional version of a Bernstein’s theorem, with complex polynomials being replaced by quaternionic polynomials. Moreover, using an Almansi-type decomposition of polynomials, we formulate the quaternionic Bernstein’s inequality in terms of four-dimensional zonal harmonics and Gegenbauer polynomials.
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