Equations with Finite-Dimensional Solution Space
In the preceding chapter on page 30 ideals of differential type zero have been introduced. The corresponding systems of pde’s are considered now. They have the distinctive property that their general solution does not involve functions depending on one or
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Texts and Monographs in Symbolic Computation A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria Series Editor: Peter Paule, RISC Linz, Austria Founding Editor: B. Buchberger, RISC Linz, Austria Editorial Board Robert Corless, University of Western Ontario, Canada Hoon Hong, North Carolina State University, USA Tetsuo Ida, University of Tsukuba, Japan Martin Kreuzer, Universit¨at Passau, Germany Bruno Salvy, INRIA Rocquencourt, France Dongming Wang, Universit´e Pierre et Marie Curie – CNRS, France
For further volumes: http://www.springer.com/series/3073
Fritz Schwarz
Loewy Decomposition of Linear Differential Equations
123
Fritz Schwarz Institute SCAI Fraunhofer Gesellschaft Sankt Augustin Germany
ISSN 0943-853X ISBN 978-3-7091-1285-4 ISBN 978-3-7091-1286-1 (eBook) DOI 10.1007/978-3-7091-1286-1 Springer Wien Heidelberg New York Dordrecht London Library of Congress Control Number: 2012945905 c Springer-Verlag Wien 2012 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 is part of Springer Science+Business Media (www.springer.com)
To Birgit
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Preface
The aim of this book is to communicate some results on solving linear differential equations that have been achieved in the last two decades. The key concept is the factorization of a differential equation or the corr
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