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Fourier Analysis Of Economic Phenomena
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Book Synopsis Fourier Analysis of Economic Phenomena by : Toru Maruyama
Download or read book Fourier Analysis of Economic Phenomena written by Toru Maruyama and published by Springer. This book was released on 2019-07-03 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations by : A.J. Jerri
Download or read book The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations written by A.J. Jerri and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Fourier Analysis by : Gerlind Plonka
Download or read book Numerical Fourier Analysis written by Gerlind Plonka and published by Springer Nature. This book was released on 2023-11-08 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classical Fourier Analysis by : Loukas Grafakos
Download or read book Classical Fourier Analysis written by Loukas Grafakos and published by Springer Science & Business Media. This book was released on 2008-09-18 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Fourier Transform Methods in Finance by : Umberto Cherubini
Download or read book Fourier Transform Methods in Finance written by Umberto Cherubini and published by John Wiley & Sons. This book was released on 2010-01-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes. Fourier Transform Methods in Finance is a practical and accessible guide to pricing financial instruments using Fourier transform. Written by an experienced team of practitioners and academics, it covers Fourier pricing methods; the dynamics of asset prices; non stationary market dynamics; arbitrage free pricing; generalized functions and the Fourier transform method. Readers will learn how to: compute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) technique characterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumps apply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniques perform a change of measure on the characteristic function in order to make the price process a martingale recover a general representation of the pricing kernel of the economy in terms of Hilbert transform using the theory of generalised functions apply the pricing formula to the most famous pricing models, with stochastic volatility and jumps. Junior and senior practitioners alike will benefit from this quick reference guide to state of the art models and market calibration techniques. Not only will it enable them to write an algorithm for option pricing using the most advanced models, calibrate a pricing model on options data, and extract the implied probability distribution in market data, they will also understand the most advanced models and techniques and discover how these techniques have been adjusted for applications in finance. ISBN 978-0-470-99400-9
Book Synopsis Contributions to Fourier Analysis. (AM-25) by : Antoni Zygmund
Download or read book Contributions to Fourier Analysis. (AM-25) written by Antoni Zygmund and published by Princeton University Press. This book was released on 2016-03-02 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Contributions to Fourier Analysis. (AM-25), will be forthcoming.
Book Synopsis Calendar by : London School of Economics and Political Science
Download or read book Calendar written by London School of Economics and Political Science and published by . This book was released on 1923 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Crises and Cycles in Economic Dictionaries and Encyclopaedias by : Daniele Besomi
Download or read book Crises and Cycles in Economic Dictionaries and Encyclopaedias written by Daniele Besomi and published by Routledge. This book was released on 2013-03-01 with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fourier Analysis in Probability Theory by : Tatsuo Kawata
Download or read book Fourier Analysis in Probability Theory written by Tatsuo Kawata and published by Academic Press. This book was released on 2014-06-17 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.
Book Synopsis E.E. Slutsky as Economist and Mathematician by : Vincent Barnett
Download or read book E.E. Slutsky as Economist and Mathematician written by Vincent Barnett and published by Routledge. This book was released on 2011-03-31 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spectral Methods in Econometrics by : George S. Fishman
Download or read book Spectral Methods in Econometrics written by George S. Fishman and published by Cambridge, Mass. : Harvard University Press. This book was released on 1969 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Essays in Econometrics by : Clive W. J. Granger
Download or read book Essays in Econometrics written by Clive W. J. Granger and published by Cambridge University Press. This book was released on 2001-07-23 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are econometrician Clive W. J. Granger's major essays in causality, integration, cointegration, and long memory.
Book Synopsis Climate Change and Circular Economics by : Ionut Purica
Download or read book Climate Change and Circular Economics written by Ionut Purica and published by Elsevier. This book was released on 2024-07-01 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Abstract Algebra: Vector Spaces by : N.B. Singh
Download or read book Abstract Algebra: Vector Spaces written by N.B. Singh and published by N.B. Singh. This book was released on with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Complex and Chaotic Nonlinear Dynamics by : Thierry Vialar
Download or read book Complex and Chaotic Nonlinear Dynamics written by Thierry Vialar and published by Springer Science & Business Media. This book was released on 2009-04-26 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines. Beyond its focus on economics and finance, including for instance the evolution of macroeconomic growth models towards nonlinear structures as well as signal processing applications to stock markets, fundamental parts of the book are devoted to the use of nonlinear dynamics in mathematics, statistics, signal theory and processing. Numerous examples and applications, almost 700 illustrations and numerical simulations based on the use of Matlab make the book an essential reference for researchers and students from many different disciplines who are interested in the nonlinear field. An appendix recapitulates the basic mathematical concepts required to use the book.
Book Synopsis Advances in Automation V by : Andrey A. Radionov
Download or read book Advances in Automation V written by Andrey A. Radionov and published by Springer Nature. This book was released on 2024-01-03 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports on innovative research and developments in automation. Spanning a wide range of disciplines, including communication engineering, power engineering, control engineering, instrumentation, signal processing and cybersecurity, it focuses on methods and findings aimed at improving the control and monitoring of industrial and manufacturing processes as well as safety. Based on the 6th International Russian Automation Conference (RusAutoCon2023), held as a hybrid conference on September 10–16, 2023, in/from Sochi, Russia, this book provides academics and professionals with a timely overview of and extensive information on the state of the art in the field of automation and control systems. It is also expected to foster new ideas and collaborations between groups in different countries.
Book Synopsis The Review of Economics and Statistics by :
Download or read book The Review of Economics and Statistics written by and published by . This book was released on 1923 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the Review is to promote the collection, criticism, and interpretation of economic statistics, with a view to making them more accurate and valuable than they are at present for business and scientific purposes.
