Approximation by polynomials in Bergman spaces of slice regular functions in the unit ball

作者：Gal S. G.; Sabadini I.^*

来源：Mathematical Methods in the Applied Sciences, 2018, 41(4): 1619-1630.

DOI：10.1002/mma.4689

• approximating polynomials
• Bergman space of the first kind
• Bergman space of the second kind
• best approximation
• convolution polynomials
• moduli of smoothness
• slice regular functions
• Taylor expansion
• quantitative estimates

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.

• 出版日期2018-3-15