Fourier Analysis of Economic Phenomena / by Toru Maruyama.
 Edition:
 1st ed. 2018.
 Publication:
 Singapore : Springer Singapore : Imprint: Springer, 2018.
 Series:
 Mathematics and Statistics (Springer11649)
Monographs in Mathematical Economics, 23648279 ; 2
Monographs in Mathematical Economics, 23648279 ; 2  Format/Description:
 Book
1 online resource (XI, 410 pages) : 64 illustrations  Subjects:
 Fourier analysis.
Economics.  Local subjects:
 Fourier Analysis. (search)
Economic Theory/Quantitative Economics/Mathematical Methods. (search)  System Details:
 text file PDF
 Summary:
 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.
 Contents:
 1. Fourier series on a Hilbert space
2. Convergence of classical Fourier series
3. Fourier transforms (1)
4. Fourier transforms (2)
5. Summation kernels and spectral syntheses
6. Fourier transforms of Radon measures
7. Spectral representations of unitary operators
8. Fourier analysis of weakly stationary stochastic processes
9. Almost periodic functions and weakly stationary stochastic processes
10. Fredholm Operators
11. Hopf bifurcations.  Contributor:
 SpringerLink (Online service)
 Contained In:
 Springer eBooks
 Other format:
 Printed edition:
Printed edition:  ISBN:
 9789811327308
9789811327308  Publisher Number:
 10.1007/9789811327308 doi
 Access Restriction:
 Restricted for use by site license.

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