Quaternionic Approximation With Application to Slice Regular Functi
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. Wit
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Sorin G. Gal Irene Sabadini
Quaternionic
Approximation: With Application to
Slice Regular Functions
Frontiers in Mathematics
Advisory Editorial Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta) William Y. C. Chen (Nankai University, Tianjin) Benoît Perthame (Sorbonne Université, Paris) Laurent Saloff-Coste (Cornell University, Ithaca) Igor Shparlinski (The University of New South Wales, Sydney) Wolfgang Sprößig (TU Bergakademie Freiberg) Cédric Villani (Institut Henri Poincaré, Paris)
More information about this series at http://www.springer.com/series/5388
Sorin G. Gal • Irene Sabadini
Quaternionic Approximation With Application to Slice Regular Functions
Sorin G. Gal Department of Mathematics and Computer Science University of Oradea Oradea, Romania
Irene Sabadini Dipartimento di Matematica Politecnico di Milano Milano, Italy
ISSN 1660-8046 ISSN 1660-8054 (electronic) Frontiers in Mathematics ISBN 978-3-030-10664-5 ISBN 978-3-030-10666-9 (eBook) https://doi.org/10.1007/978-3-030-10666-9 Mathematics Subject Classification (2010): 30G35, 30E05, 30E10, 41A10, 41A17, 41A25 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface Complex analysis is very rich in approximation theory results. In this Preface we briefly list some of them which are nowadays considered classical, with no pretense of completeness, the aim being to show what type of problems we shall discuss in this monograph. One important result, obtained by Stone [181], is the extension of the Weierstrass theorem to approximate complex-valued continuous functions defined on a compact Hausdorff space. Continuous complex-va
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