Quaternionic Approximation

With Application to Slice Regular Functions
1. Auflage 2019
ISBN: 978-3-030-10664-5
Verlag: Springer International Publishing

Buch, Englisch, 221 Seiten, Format (B × H): 168 mm x 240 mm, Gewicht: 397 g

Reihe: 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.

Zielgruppe

Research

Autoren/Hrsg.

Sabadini, Irene

Gal, Sorin G.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Preliminaries on Hypercomplex Analysis.- Approximation of Continuous Functions.- Approximation 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.