Quaternionic Approximation: With Application to Slice Regular Functions

✍ Scribed by Sorin G. Gal, Irene Sabadini

Publisher: Springer International Publishing; Birkhäuser
Year: 2019
Tongue: English
Leaves: 228
Series: Frontiers in Mathematics
Edition: 1st ed.
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Mathematics; Functions of a Complex Variable; Approximations and Expansions

📜 SIMILAR VOLUMES

Entire Slice Regular Functions

📁 Entire Slice Regular Functions

✍ Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa 📂 Library 📅 2016 🏛 BIRKHAUSER Verlag AG;Springer 🌐 English

This Briefs volume develops the theory of entire slice regular functions. It is the first self-contained, monographic work on the subject, offering all the necessary background information and detailed studies on several central topics, including estimates on the minimum modulus of regular functi

Entire Slice Regular Functions

📁 Entire Slice Regular Functions

✍ Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa (auth.) 📂 Library 📅 2016 🏛 Springer International Publishing 🌐 English

This Briefs volume develops the theory of entire slice regular functions. It is the first self-contained, monographic work on the subject, offering all the necessary background information and detailed studies on several central topics, including estimates on the minimum modulus of regular fun

Regular functions of a quaternionic vari

📁 Regular functions of a quaternionic variable

✍ Graziano Gentili; Caterina Stoppato; Daniele C Struppa 📂 Library 📅 2013 🏛 Springer 🌐 English

Introduction.- 1.Definitions and Basic Results.- 2.Regular Power Series.- 3.Zeros.- 4.Infinite Products.- 5.Singularities.- 6.Integral Representations.- 7.Maximum Modulus Theorem and Applications.- 8.Spherical Series and Differential.- 9.Fractional Transformations and the Unit Ball.- 10.Generalizat

Regular Functions of a Quaternionic Vari

📁 Regular Functions of a Quaternionic Variable

✍ Graziano Gentili, Caterina Stoppato, Daniele C. Struppa (auth.) 📂 Library 📅 2013 🏛 Springer-Verlag Berlin Heidelberg 🌐 English

The theory of slice regular functions over quaternions is the central subject of the present volume. This recent theory has expanded rapidly, producing a variety of new results that have caught the attention of the international research community. At the same time, the theory has already deve

Regular Functions of a Quaternionic Vari

📁 Regular Functions of a Quaternionic Variable

✍ Graziano Gentili, Caterina Stoppato, Daniele C. Struppa 📂 Library 📅 2022 🏛 Springer 🌐 English

This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications.As in the case of other interesting quaternionic function theories, the original motivations

Regular Functions of a Quaternionic Vari

📁 Regular Functions of a Quaternionic Variable

✍ Graziano Gentili, Caterina Stoppato, Daniele C. Struppa 📂 Library 📅 2022 🏛 Springer 🌐 English