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.
A quaternionic Bernstein theorem / Perotti, Alessandro. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5454. - 20:(2023), pp. 15401-15410. [10.1007/s00009-023-02362-w]
A quaternionic Bernstein theorem
Perotti, Alessandro
2023-01-01
Abstract
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.File in questo prodotto:
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