Gal S.G., Sabadini I. Quaternionic Approximation: With Application to Slice Regular Functions

Springer, 2019. — 228 p. — (Frontiers in Mathematics). — ISBN: 978-3-030-10664-5.This book presents the extensions to the quaternionic setting of some of the main approximation results in complex analysis. It also includes the main inequalities regarding the behavior of the derivatives of polynomials with quaternionic cofficients. With some few exceptions, all the material in this book belongs to recent research of the authors on the approximation of slice regular functions of a quaternionic variable.
The book is addressed to researchers in various areas of mathematical analysis, in particular hypercomplex analysis, and approximation theory. It is accessible to graduate students and suitable for graduate courses in the above framework.Preliminaries on Hypercomplex Analysis
Approximation of Continuous Functions
Approximation in Compact Balls by Bernstein and Convolution Type Operators
Approximation of Slice Regular Functions in Compact Sets
Overconvergence, Equiconvergence and Universality Properties
Inequalities for Quaternionic Polynomials
Approximation of nullsolutions of generalized Cauchy–Riemann operators