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Approximation by polynomials in Bergman spaces of slice regular functions in the unit ball
Author(s) -
Gal S. G.,
Sabadini I.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4689
Subject(s) - mathematics , unit sphere , constructive , ball (mathematics) , smoothness , mathematical proof , convolution (computer science) , pure mathematics , moduli , mathematical analysis , taylor series , geometry , physics , process (computing) , quantum mechanics , machine learning , computer science , artificial neural network , operating system
In this paper, we show that the set of quaternionic polynomials is dense in the Bergman spaces of slice regular functions in the unit ball, both of the first and of the second kind. Several proofs are presented, including constructive methods based on the Taylor expansion and on the convolution polynomials. In the last case, quantitative estimates in terms of higher‐order moduli of smoothness and of best approximation quantity are obtained.