Fourier Analysis of Economic Phenomena
Authors: Maruyama, Toru
 Is the first book to explain how to apply Fourier analysis in business cycle theory in a mathematically rigorous manner
 Provides an explanation of Fourier analysis of generalized functions, which is indispensable for business cycle theory
 Presents indepth proofs of Bochner's theorem, a difficult theorem but one with great importance in Fourier analysis
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 About this book

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 focus is on a couple of trials: (1) the Kaldor theory and (2) the Slutsky effect. The Kaldor theory tries to explain business fluctuations in terms of nonlinear, 2ndorder ordinary differential equations (ODEs). In order to explain periodic behaviors of a solution, the Hopfbifurcation theorem frequently plays a key role. Slutsky's idea is to look at the periodic movement as an overlapping effect of random shocks. The Slutsky process is a weakly stationary process, the periodic (or almost periodic) behavior of which can be analyzed by the Bochner theorem. The goal of this book is to give a comprehensive and rigorous justification of these ideas. Therefore, the aim is first to give a complete theory that supports the Hopf theorem and to prove the existence of periodic solutions of ODEs; and second to explain the mathematical structure of the Bochner theorem and its relation to periodic (or almost periodic) behaviors of weakly stationary processes.Although these two targets are the principal ones, a large number of results from Fourier analysis must be prepared in order to reach these goals. The basic concepts and results from classical as well as generalized Fourier analysis are provided in a systematic way.Prospective readers are assumed to have sufficient knowledge of real, complex analysis. However, necessary economic concepts are explained in the text, making this book accessible even to readers without a background in economics.
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Bibliographic Information
 Bibliographic Information

 Book Title
 Fourier Analysis of Economic Phenomena
 Authors

 Toru Maruyama
 Series Title
 Monographs in Mathematical Economics
 Series Volume
 2
 Copyright
 2018
 Publisher
 Springer Singapore
 Copyright Holder
 Springer Nature Singapore Pte Ltd.
 eBook ISBN
 9789811327308
 DOI
 10.1007/9789811327308
 Hardcover ISBN
 9789811327292
 Series ISSN
 23648279
 Edition Number
 1
 Number of Pages
 XI, 410
 Number of Illustrations
 30 b/w illustrations
 Topics