Quaternionic Approximation: With Application to Slice Regular Functions (Frontiers in Mathematics)

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. Front Matter ....Pages i-x Preliminaries on Hypercomplex Analysis (Sorin G. Gal, Irene Sabadini)....Pages 1-24 Approximation of Continuous Functions (Sorin G. Gal, Irene Sabadini)....Pages 25-36 Approximation in Compact Balls by Bernstein and Convolution Type Operators (Sorin G. Gal, Irene Sabadini)....Pages 37-81 Approximation of Slice Regular Functions in Compact Sets (Sorin G. Gal, Irene Sabadini)....Pages 83-128 Overconvergence, Equiconvergence and Universality Properties (Sorin G. Gal, Irene Sabadini)....Pages 129-160 Inequalities for Quaternionic Polynomials (Sorin G. Gal, Irene Sabadini)....Pages 161-185 Approximation of nullsolutions of generalized Cauchy–Riemann operators (Sorin G. Gal, Irene Sabadini)....Pages 187-203 Back Matter ....Pages 205-221