Continuous Nowhere Differentiable Functions The Monsters of Analysis
This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the
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Marek Jarnicki Peter Pflug
Continuous Nowhere Differentiable Functions The Monsters of Analysis
Springer Monographs in Mathematics
More information about this series at http://www.springer.com/series/3733
Marek Jarnicki • Peter Pflug
Continuous Nowhere Differentiable Functions The Monsters of Analysis
123
Marek Jarnicki Institute of Mathematics Jagiellonian University Krak´ow, Poland
Peter Pflug Insitute for Mathematics Carl von Ossietzky University Oldenburg Oldenburg, Germany
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-319-12669-2 ISBN 978-3-319-12670-8 (eBook) DOI 10.1007/978-3-319-12670-8 Library of Congress Control Number: 2015955827 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Preface
As its title indicates, this book aims to be a comprehensive, self-contained compendium of results on continuous nowhere differentiable functions, collecting many results hitherto accessible only in the scattered literature.
Motivation for Writing This Book Why did the authors, both specialists in several complex variables, decide to write a book on continuous nowhere differentiable functions? Let us try to answer this question: (a) Whenever we would give a lecture on real analysis, we felt unsatisfied, since there was almost no time to discuss continuous nowhere differentiable functions in detail. Therefore, we could only mention the existence of such functions in most of our lectures. Moreover, whenever we wanted to deal with such functions in a proseminar, it was difficult to find a source book. Some information could be found in a master’s thesis by J. Thim (see [Thi03]), which presented a more detailed description of these functions. Later, during the writing of this book, we found another
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