An Introduction to Ultrametric Summability Theory
This is the second, completely revised and expanded edition of the author’s first book, covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of mathematics in recen
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P.N. Natarajan
An Introduction to Ultrametric Summability Theory Second Edition
Forum for Interdisciplinary Mathematics Volume 2
Editor-in-chief P.V. Subrahmanyam, Indian Institute of Technology Madras, Chennai, India Editorial Board Bhu Dev Sharma, Forum for Interdisciplinary Mathematics, Meerut, India Janusz Matkowski, University of Zielona Góra, Zielona Góra, Poland Mathieu Dutour Sikirić, Institute Rudjer Boúsković, Zagreb, Croatia Thiruvenkatachari Parthasarathy, Chennai Mathematical Institute, Kelambakkam, India Yogendra Prasad Chaubey, Concordia University, Montréal, Canada
The Forum for Interdisciplinary Mathematics (FIM) series publishes high-quality monographs and lecture notes in mathematics and interdisciplinary areas where mathematics has a fundamental role, such as statistics, operations research, computer science, financial mathematics, industrial mathematics, and biomathematics. It reflects the increasing demand of researchers working at the interface between mathematics and other scientific disciplines.
More information about this series at http://www.springer.com/series/13386
P.N. Natarajan
An Introduction to Ultrametric Summability Theory Second Edition
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P.N. Natarajan Formerly of the Department of Mathematics Ramakrishna Mission Vivekananda College Chennai, Tamil Nadu India
ISSN 2364-6748 ISSN 2364-6756 (electronic) Forum for Interdisciplinary Mathematics ISBN 978-81-322-2558-4 ISBN 978-81-322-2559-1 (eBook) DOI 10.1007/978-81-322-2559-1 Library of Congress Control Number: 2015945119 Springer New Delhi Heidelberg New York Dordrecht London © Springer India 2014, 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 (India) Pvt. Ltd. is part of Springer Science+Business Media (www.springer.com)
Dedicated to my parents S. Thailambal and P.S. Narayanasubramanian
Preface to the Second Edition
Most of the material discussed in the present revised, enlarged edition has appeared in the first edition of the book,
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