Advances in Applied Clifford Algebras, volume 30, issue 5, publication number 64
Polynomial Approximation in Quaternionic Bloch and Besov Spaces
Sorin G. Gal
1, 2
,
Irene Sabadini
3
1
Department of mathematics and Computer Science, University of Oradea, Oradea, Romania
|
2
The Academy of Romanian Scientists, Bucharest, Romania
|
Publication type: Journal Article
Publication date: 2020-09-10
scimago Q3
SJR: 0.414
CiteScore: 2.2
Impact factor: 1.1
ISSN: 01887009, 16614909
Applied Mathematics
Abstract
In this paper we continue our study on the density of the set of quaternionic polynomials in function spaces of slice regular functions on the unit ball by considering the case of the Bloch and Besov spaces of the first and of the second kind. Among the results we prove, we show some constructive methods based on the Taylor expansion and on the convolution polynomials. We also provide quantitative estimates in terms of higher order moduli of smoothness and of the best approximation quantity. As a byproduct, we obtain two new results for complex Bloch and Besov spaces.
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