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Polynomial approximation in quaternionic Bloch and Besov spaces. (English) Zbl 1455.30039

This paper continues a series of investigations by the authors about quaternionic approximation (see also the book of the authors [Quaternionic approximation. With application to slice regular functions. Cham: Birkhäuser (2019; Zbl 1432.30034)]).
In this paper the authors work with quaternionic generalizations of Bloch and Besov spaces on the unit ball. For each of the spaces they prove a theorem on approximation by polynomials. When possible they also give quantitative results on the reminder of the approximation.
As the other papers in the same series, this one is also well detailed and gives several links to the standard complex theory.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
30E10 Approximation in the complex plane

Citations:

Zbl 1432.30034
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References:

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