Fourier Analysis of Economic Phenomena
Fourier Analysis of Economic Phenomena

Author: Toru Maruyama

Publisher: Springer

Published: 2019-07-03

Total Pages: 413

ISBN-13: 9811327300

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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, 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.

The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations
The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations

Author: A.J. Jerri

Publisher: Springer Science & Business Media

Published: 1998-08-31

Total Pages: 376

ISBN-13: 9780792351092

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This book represents the first attempt at a unified picture for the pres ence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out. The analysis and filtering cover the familiar Gibbs phenomenon in Fourier series and integral representations of functions with jump discontinuities. In ad dition it will include other representations, such as general orthogonal series expansions, general integral transforms, splines approximation, and continuous as well as discrete wavelet approximations. The mate rial in this book is presented in a manner accessible to upperclassmen and graduate students in science and engineering, as well as researchers who may face the Gibbs phenomenon in the varied applications that in volve the Fourier and the other approximations of functions with jump discontinuities. Those with more advanced backgrounds in analysis will find basic material, results, and motivations from which they can begin to develop deeper and more general results. We must emphasize that the aim of this book (the first on the sUbject): to satisfy such a diverse audience, is quite difficult. In particular, our detailed derivations and their illustrations for an introductory book may very well sound repeti tive to the experts in the field who are expecting a research monograph. To answer the concern of the researchers, we can only hope that this book will prove helpful as a basic reference for their research papers.

Classical Fourier Analysis
Classical Fourier Analysis

Author: Loukas Grafakos

Publisher: Springer Science & Business Media

Published: 2008-09-18

Total Pages: 494

ISBN-13: 0387094326

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The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). From a review of the first edition: “Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online

Numerical Fourier Analysis
Numerical Fourier Analysis

Author: Gerlind Plonka

Publisher: Springer Nature

Published: 2023-11-08

Total Pages: 676

ISBN-13: 3031350057

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New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.

Calendar
Calendar

Author: London School of Economics and Political Science

Publisher:

Published: 1923

Total Pages: 270

ISBN-13:

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Crises and Cycles in Economic Dictionaries and Encyclopaedias
Crises and Cycles in Economic Dictionaries and Encyclopaedias

Author: Daniele Besomi

Publisher: Routledge

Published: 2013-03-01

Total Pages: 908

ISBN-13: 1136722890

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This book aims at investigating from the perspective of the major economic dictionaries the notions of economic crisis and cycle. The project consists in giving an extensive summary of a number of significant entries on this subject, with an introductory essay to each entry placing them (and the dictionary to which they belong) in their context, giving some details on the author of the dictionary entry, and assessing the entry’s (and its author’s) contribution. The broad picture (including the history of these encyclopedic tools) will be examined in the introductory essays.

E.E. Slutsky as Economist and Mathematician
E.E. Slutsky as Economist and Mathematician

Author: Vincent Barnett

Publisher: Routledge

Published: 2011-03-31

Total Pages: 262

ISBN-13: 1136737316

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E.E. Slutsky is perhaps the Russian/Ukrainian economist most quoted by mainstream economists today. This is the first research monograph to examine the life and work of the internationally-renowned economist and mathematician. It does so from both a ‘history of economics’ perspective and a ‘history of science’ perspective, bringing these two strands together in order to demonstrate Slutsky’s enduring legacy as an innovative researcher and an influential intellectual. It also presents some of Slutsky’s lesser-known (and hitherto-unavailable) works in English translation.

Essays in Econometrics
Essays in Econometrics

Author: Clive W. J. Granger

Publisher: Cambridge University Press

Published: 2001-07-23

Total Pages: 400

ISBN-13: 9780521796491

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These are econometrician Clive W. J. Granger's major essays in causality, integration, cointegration, and long memory.

Climate Change and Circular Economics
Climate Change and Circular Economics

Author: Ionut Purica

Publisher: Elsevier

Published: 2024-06-19

Total Pages: 306

ISBN-13: 0443299706

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Climate Change and Circular Economics: Human Society as a Closed Thermodynamic System aims to go beyond the concept of 'fighting climate change' to analyze the capacity of human society to evolve in relation to the environment based on a more complex approach. The book stresses the role of resource recovery by innovation in reducing the temperature increase, determined through an irreversible thermodynamic approach. Determining the speed of temperature increase contributed by selected economies and comparing these to environmental recovery time constants shows that emerging economies have a much greater speed and consequently a larger impact on environmental capability to recover.Chapters progress from an analysis of present society as a dissipative open system to a thermodynamics view of the need for a circular economy, a big data analysis of climate change and risk mitigation, economic indicators, including entropy and economics, risk maps of climate change events risks, and insights into the 'Gibbs paradox', which describes the connection of two separate systems (like society and environment). - Offers a unique, intersectional perspective on climate change - Introduces generational risk maps for climate change events, opening the possibility for insurance as well as other mitigation and adaptation policies - Provides methods to determine the contribution of selected economies to temperature increase and speed of increase using irreversible thermodynamics that allows for comparison with environmental recovery time constants - Ends with a solution of the Gibbs 'paradox' that relies not on binary logic, but rather a multivalued modal logic of possibilities that sheds a profound light on the interaction of separate spaces versus their combination

Abstract Algebra: Vector Spaces
Abstract Algebra: Vector Spaces

Author: N.B. Singh

Publisher: N.B. Singh

Published:

Total Pages: 121

ISBN-13:

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"Abstract Algebra: Vector Spaces" is a comprehensive exploration of vector spaces within the realm of abstract algebra, offering a clear and insightful journey into foundational concepts and their diverse applications. From fundamental definitions of basis and dimension to advanced topics like quantum mechanics, coding theory, and data science, this book equips readers with a robust understanding of how vector spaces underpin various theoretical frameworks and real-world problems. With an emphasis on clarity and practical relevance, it serves as an invaluable resource for students, researchers, and enthusiasts seeking to deepen their knowledge and explore the profound connections between algebraic structures and modern applications.