Real Quaternionic Calculus Handbook
Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, such as complex analysis, harm
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eal Quaternionic Calculus Handbook
João Pedro Morais Svetlin Georgiev Wolfgang Sprößig
Real Quaternionic Calculus Handbook
João Pedro Morais CIDMA University of Aveiro Aveiro Portugal Wolfgang Sprößig Institut für Angewandte Analysis TU Bergakademie Freiberg Freiberg Germany
Svetlin Georgiev Department of Differential Equations University of Sofia St Kliment Ohridski Faculty of Mathematics and Informatics Sofia, Bulgaria
ISBN 978-3-0348-0621-3 ISBN 978-3-0348-0622-0 (eBook) DOI 10.1007/978-3-0348-0622-0 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2013957805 Mathematics Subject Classification 2010: 17C60, 30G35, 05A05, 15A66, 15A54, 51M05 c Springer Basel 2014 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer Basel is part of Springer Science+Business Media (www.springer.com)
Preface
Real Quaternionic Analysis is a multifaceted subject. Created to describe some phenomena in special relativity, electrodynamics, spin, etc. It has developed into a body of material that interacts with many branches of mathematics, such as complex analysis, harmonic analysis, differential geometry, differential equations, as well as into a ubiquitous factor in the description and elucidation of problems in mathematical physics. Quaternions have been towards Maxwell’s equations. In the meantime, rea
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