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Harmonic studies and analysis of industrial and commercial power systems are described. The basic concepts involved in such studies are described first. This is followed by a discussion of how to determine the need for a harmonic study, how to assemble the required data, how to recognize potential problems, and how to implement corrective measures.

Harmonic analysis.

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Finite fields (Algebra). --- Finite groups. --- Fourier transformations. --- Harmonic analysis.

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This book, intended to commemorate the work of Paul Dirac, highlights new developments in the main directions of Clifford analysis. Just as complex analysis is based on the algebra of the complex numbers, Clifford analysis is based on the geometric Clifford algebras. Many methods and theorems from complex analysis generalize to higher dimensions in various ways. However, many new features emerge in the process, and much of this work is still in its infancy. Some of the leading mathematicians working in this field have contributed to this book in conjunction with “Clifford Analysis and Related Topics: a conference in honor of Paul A.M. Dirac,” which was held at Florida State University, Tallahassee, on December 15-17, 2014. The content reflects talks given at the conference, as well as contributions from mathematicians who were invited but were unable to attend. Hence much of the mathematics presented here is not only highly topical, but also cannot be found elsewhere in print. Given its scope, the book will be of interest to mathematicians and physicists working in these areas, as well as students seeking to catch up on the latest developments.

Algebraic geometry --- Harmonic analysis. Fourier analysis --- Mathematical analysis --- analyse (wiskunde) --- complexe veranderlijken --- Fourierreeksen --- mathematische modellen --- wiskunde

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This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis. Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, Lp spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.

Functional analysis --- Harmonic analysis. Fourier analysis --- Mathematical analysis --- Mathematics --- Fourieranalyse --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde

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Essentials of Time Series for Financial Applications serves as an agile reference for upper level students and practitioners who desire a formal, easy-to-follow introduction to the most important time series methods applied in financial applications (pricing, asset management, quant strategies, and risk management). Real-life data and examples developed with EViews illustrate the links between the formal apparatus and the applications. The examples either directly exploit the tools that EViews makes available or use programs that by employing EViews implement specific topics or techniques. The book balances a formal framework with as few proofs as possible against many examples that support its central ideas. Boxes are used throughout to remind readers of technical aspects and definitions and to present examples in a compact fashion, with full details (workout files) available in an on-line appendix. The more advanced chapters provide discussion sections that refer to more advanced textbooks or detailed proofs. Provides practical, hands-on examples in time-series econometrics Presents a more application-oriented, less technical book on financial econometrics Offers rigorous coverage, including technical aspects and references for the proofs, despite being an introduction Features examples worked out in EViews (9 or higher)

Time-series analysis. --- Econometrics. --- Economics, Mathematical --- Statistics --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Mathematical statistics --- Probabilities