Fourier Analysis of Economic Phenomena
This is the first monograph that discusses in detail the interactions between Fourier analysis and dynamic economic theories, in particular, business cycles.Many economic theories have analyzed cyclical behaviors of economic variables. In this book, the f
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Toru Maruyama
Fourier Analysis of Economic Phenomena
Monographs in Mathematical Economics Volume 2
Editor-in-chief Toru Maruyama, Tokyo, Japan Series editors Shigeo Kusuoka, Tokyo, Japan Jean-Michel Grandmont, Malakoff, France R. Tyrrell Rockafellar, Seattle, USA
More information about this series at http://www.springer.com/series/13278
Toru Maruyama
Fourier Analysis of Economic Phenomena
123
Toru Maruyama Professor Emeritus Keio University Tokyo, Japan
ISSN 2364-8279 ISSN 2364-8287 (electronic) Monographs in Mathematical Economics ISBN 978-981-13-2729-2 ISBN 978-981-13-2730-8 (eBook) https://doi.org/10.1007/978-981-13-2730-8 Library of Congress Control Number: 2018958313 © Springer Nature Singapore Pte Ltd. 2018 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
Fourier analysis as a branch of mathematical analysis was born from ingenious attempt to express a function as a weighted sum of trigonometric waves. In particular, abstract theory addressing a similar problem on topological groups is sometimes called harmonic analysis. However, Fourier analysis and harmonic analysis are almost synonymous, and we do not distinguish between these two names in this book. The interaction between Fourier analysis and other fields of mathematics has a long and remarkable history. The role of Fourier analysis in physics has also been impossible to exaggerate. However, the situation is quite different regarding its relation with economics. Indeed, Fourier analysis has not been so familiar to economists, except for specialists of time series analysis. Therefore, we have to confess that the extent of the interaction between Fourier analysis and economics is quite
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