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000898395 020__ $$a9789811327308$$q(electronic book)
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000898395 0248_ $$a10.1007/978-981-13-2
000898395 035__ $$aSP(OCoLC)on1107667215
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000898395 08204 $$a515.2433$$223
000898395 1001_ $$aMaruyama, Toru,$$eauthor.
000898395 24510 $$aFourier analysis of economic phenomena /$$cToru Maruyama.
000898395 264_1 $$aSingapore :$$bSpringer,$$c[2018]
000898395 300__ $$a1 online resource.
000898395 336__ $$atext$$btxt$$2rdacontent
000898395 337__ $$acomputer$$bc$$2rdamedia
000898395 338__ $$aonline resource$$bcr$$2rdacarrier
000898395 4901_ $$aMonographs in mathematical economics,$$x2364-8287 ;$$vvolume 2
000898395 504__ $$aIncludes bibliographical references and index.
000898395 5050_ $$a1. 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.
000898395 506__ $$aAccess limited to authorized users.
000898395 520__ $$aThis 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, 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 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.
000898395 588__ $$aOnline resource; title from PDF title page (viewed July 9, 2019).
000898395 650_0 $$aFourier analysis.
000898395 650_0 $$aEconomics.
000898395 830_0 $$aMonographs in mathematical economics ;$$vv. 2.
000898395 852__ $$bebk
000898395 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-981-13-2730-8$$zOnline Access$$91397441.1
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