Quaternionic approximation: with application to slice regular functions
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 ana…
Read More ↓Title Statements
- Full title :Quaternionic approximation : with application to slice regular functions / Sorin G. Gal, Irene Sabadini.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2019.
Publication Statements
- Publisher(s):Birkhäuser
- Place of Publication:Cham, Switzerland
- Language:eng
- Publication Date:2019.
The Physical Object
- Description:1 online resource (x, 221 pages)
Edition Identifiers
- ISBN:9783030106669, 3030106667
- DOI:10.1007/978-3-030-10666-9
- oclc:on1098041570
- LC Classification:QA331.7
- Dewey Decimal:515/.9
Table of Contents
Intro; Preface; Contents; Chapter 1 Preliminaries on Hypercomplex Analysis; 1.1 An introduction to slice regular functions; 1.2 Slice regular functions, an alternative definition; 1.3 Further properties of slice regular functions; 1.4 Preliminary results on quaternionic polynomials; 1.5 Slice monogenic functions; 1.6 Other hypercomplex function theories; 1.7 A connection between theories of hyperholomorphy via the Fueter mapping theorem; Chapter 2 Approximation of Continuous Functions; 2.1 Weierstrass-Stone Type Results; 2.2 Carleman Type Results; 2.3 Notes on Müntz-Szász Type Results
Chapter 3 Approximation in Compact Balls by Bernstein and Convolution Type Operators3.1 Approximation by q-Bernstein Polynomials, q≥1, in Compact Balls; 3.2 Approximation in Compact Balls and in Cassini Cells; 3.2.1 Approximation by quaternionic polynomial convolutions; 3.2.2 Approximation by nonpolynomial quaternion convolutions; 3.2.3 Approximation by convolution operators of a paravector variable; Chapter 4 Approximation of Slice Regular Functions in Compact Sets; 4.1 Runge Type Results; 4.2 Mergelyan Type Results; 4.2.1 Riemann mappings for axially symmetric sets
4.2.2 Approximation in some par…
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