Analysis
The chapter on functional analysis is arranged so that when any concept of functional analysis is needed at a particular place, its definition can always be found beforehand.
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Handbook of Mathematics
Springer-Verlag Berlin Heidelberg GmbH
I. N. Bronshtein · K. A. Semendyayev
Handbook of Mathematics English translation edited by K. A. Hirsch Reprint of the third edition
i
Springer
Editors: Dr. G. Grosche and Dr. V. Ziegler
The new version of the Handbook was written or revised by: P. Beckmann (2.6.3., 2.6.4.) M. Belger (3.4.) H. Benker (3.2.1.) N. Denkmann (7.2.3.) M. Dewess (6.) H. Erfurth (3.2.2.) H. Gentemann (3.4.) S. Gottwald (4.1.) G. Grosche (1.2., 1.3., 2.1., 2.3., 2.4.1., 2.6.1., 2.6.2., 7.2.2.)
H. Hilbing (3.1.7·-3·1.13.) R. Hofmann (7.1.) H. Kastner (2.4.2.-2.4.4·) W. Purkert (4.4., 5.) J. vom Scheidt (3.1.14., 3.1.15., 3.3.) K. A. Semendyayev (4.4·1.3., 7.2.1.) T. Vettermann (2.6.5., 2.6.6.) V. Wiinsch (3.1.1.- 3.1.6.) E. Zeidler (4.2., 4.3.)
English version edited by Professor K. A. Hirsch with the collaboration of E. J. F. Primrose A.M. Tropper S. K. Zaremba
A.Cerf A.l. Mcisaac 0. Pretzel
Reprint of the third completely revised edition of Bronshtein/Semendyayev, Handbook of Mathematics, based 19/20 German edition of Bronshtein/Semendyayev,
Taschenbuch der Mathematik
First published under the title Spravochnik po matematike dlya inshenerov i vchashchikhaya vtuzov by NAUKA, Moscow
ISBN 978-3-662-21984-3 ISBN 978-3-662-21982-9 (eBook) DOI 10.1007/978-3-662-21982-9 This work is subject to copyright. All rights are reserved, whether tile whole or part of the material is concerned, specifically tile rights oftranslation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication oftllis publication or parts thereof is permitted only under tile provisions of tile German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution act under German Copyright Law. ©Springer-Verlag Berlin Heidelberg 1998 Originally published by Springer-Verlag Berlin Heidelberg New York in 1998 Softcover reprint of the hardcover 3rd edition 1998 The use of general descriptive names, registered names, trademarks, etc. in tllis 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. 60/3020 - 5 4 3 2 1 - Printed on acid-free paper
Preface of the Reprint of the 3rd edition
The book is in such high demand that the publisher decided to reprint the 3rd edition published in 1997. January 1997
Springer- Verlag
Preface
Tn 1957 one of the two Editors translated the Handbook of Mathematics by I. N. Bronshtein and K. A. Semendyayev from Russian into German. In comparison with the original, there were two additional sections "Calculus of v.. riation" and "Integral equations". Over the years this book has become a standard work also in German speaking countries. For nearly two decades it was an indispensable help for many students, teachers and practitione