Polynomial Approximation in Slice Regular Fock Spaces

Abstract

The main purpose of this paper is to prove some density results of polynomials in Fock spaces of slice regular functions. The spaces can be of two different kinds since they are equipped with different inner products and contain different functions. We treat both the cases, providing several results, some of them based on constructive methods which make use of the Taylor expansion and of the convolution polynomials. We also prove quantitative estimates in terms of higher order moduli of smoothness and in terms of the best approximation quantities. , Fock space of the first kind, Fock space of the second kind, approximating polynomials, Taylor expansion, convolution polynomials, quantitative estimates, moduli of smoothness, best approximation. * Marie Sklodowska-Curie fellow of the Istituto Nazionale di Alta Matematica

Approximation by Convolution Polyanalytic Operators in the Complex and Quaternionic Compact Unit Balls

“…To obtain our results, we use the classical method of convolution with various even trigonometric kernels and with the Gauss-Weierstrass kernels, successfully used by us in the past, see, e.g., Gal [22][23][24], Gal-Sabadini [27][28][29][30][31], Diki-Gal-Sabadini [17].…”