Overview
- 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 in-depth proofs of Bochner's theorem, a difficult theorem but one with great importance in Fourier analysis
Part of the book series: Monographs in Mathematical Economics (MOME, volume 2)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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, 2nd-order ordinary differential equations (ODEs). In order to explain periodic behaviors of a solution, the Hopf-bifurcation 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 Hopftheorem 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.
Reviews
“The manuscript is a well balanced collection of economic applications and systematic and carefully constructed mathematical theories. Among the various economic theories on business, the fluctuations model is considered the most typical and influential. The manuscript includes fluctuations from both theoretical and empirical viewpoints. … The manuscript ‘Fourier analysis of economic phenomena’ is a very good auxiliary text book for graduate finance, business, and administrative sciences, graduate mathematical modeling, and applied mathematics.” (Haydar Akca, zbMATH 1473.42001, 2021)
“This book is of interest to researchers in various fields who use mathematical models that require the use of Fourier analysis.” (Ants Aasma, Mathematical Reviews, August, 2020)
Authors and Affiliations
Bibliographic Information
Book Title: Fourier Analysis of Economic Phenomena
Authors: Toru Maruyama
Series Title: Monographs in Mathematical Economics
DOI: https://doi.org/10.1007/978-981-13-2730-8
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-13-2729-2Published: 15 July 2019
eBook ISBN: 978-981-13-2730-8Published: 03 July 2019
Series ISSN: 2364-8279
Series E-ISSN: 2364-8287
Edition Number: 1
Number of Pages: XI, 410
Number of Illustrations: 64 b/w illustrations
Topics: Fourier Analysis, Economic Theory/Quantitative Economics/Mathematical Methods