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This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a - reasonably self-contained - exposition of Plancherel theory. Therefore, the book can also be read as a problem-driven introduction to the Plancherel formula.

Harmonic analysis. Fourier analysis --- Fourieranalyse

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E. Magenes: Il problema della derivata obliqua regolare per le equazioni lineari ellittico-paraboliche del secondo ordine in m variabili.- G. Stampacchia: Completamenti funzionali ed applicazione alla teoria dei potenziali di dominio.- A. Zygmund: On regular integrals.- S. Faedo: Applicazione ai problemi di derivata obliqua di un principio esistenziale e di una legge di dualità fra le formule di maggiorazione.- G. Fichera: Una introduzione alla teoria delle equazioni integrali singolari.

Harmonic analysis. Fourier analysis --- Partial differential equations --- Fourieranalyse --- differentiaalvergelijkingen

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The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition of new material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation, Fourier Series, the Fourier Transform, Maximal Functions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals of Nonconvolution Type, and Weighted Inequalities. These volumes are mainly addressed to graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. The prerequisites for the first volume are satisfactory completion of courses in real and complex variables. The second volume assumes material from the first. This book is intended to present the selected topics in 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. About the first edition: "Grafakos's book is very user-friendly with numerous examples illustrating the definitions and ideas... 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." - Kenneth Ross, MAA Online

Functional analysis --- Harmonic analysis. Fourier analysis --- Mathematical analysis --- Fourieranalyse --- analyse (wiskunde) --- Fourierreeksen --- functies (wiskunde) --- mathematische modellen --- Harmonic analysis

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'A First Course in Statistics for Signal Analysis' is a small, dense, and inexpensive book that covers exactly what the title says: statistics for signal analysis. The book has much to recommend it. The author clearly understands the topics presented. The topics are covered in a rigorous manner, but not so rigorous as to be ostentatious. The sequence of topics is clearly targeted at the spectral properties of Gaussian stationary signals. Any student studying traditional communications and signal processing would benefit from an understanding of these topics...In summary, [the work] has much in its favor...This book is most appropriate for a graduate class in signal analysis. It also could be used as a secondary text in a statistics, signal processing, or communications class. JASA> (Review of the First Edition) This essentially self-contained, deliberately compact, and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, explained in a concise, yet fairly rigorous presentation. Topics and Features: Fourier series and transforms fundamentally important in random signal analysis and processing are developed from scratch, emphasizing the time-domain vs. frequency-domain duality; Basic concepts of probability theory, laws of large numbers, the central limit theorem, and statistical parametric inference procedures are presented so that no prior knowledge of probability and statistics is required; the only prerequisite is a basic two-three semester calculus sequence; Computer simulation algorithms of stationary random signals with a given power spectrum density; Complementary bibliography for readers who wish to pursue the study of random signals in greater depth; Many diverse examples and end-of-chapter problems and exercises. New to the Second Edition: Revised notation and terminology to better reflect the concepts under discussion; Many redrawn figures to better illustrate the scale of the quantities represented; Considerably expanded sections with new examples, illustrations, and commentary; Addition of more applied exercises; A large appendix containing solutions of selected problems from each of the nine chapters. Developed by the author over the course of many years of classroom use, A First Course in Statistics for Signal Analysis, Second Edition may be used by junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. The work is also an excellent resource of educational and training material for scientists and engineers working in research laboratories.

Statistical science --- Harmonic analysis. Fourier analysis --- Mathematics --- Computer. Automation --- beeldverwerking --- Fourieranalyse --- toegepaste wiskunde --- signaalverwerking --- statistisch onderzoek

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I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time. Proceedings of the IEEE It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one. Computing Reviews I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets. Physics Today This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing. SIAM Review The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field. Mathematical Reviews The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis. Internationale Mathematische Nachrichten For additional review samples and related material, please visit the author's website at www.wavelets.com.

Harmonic analysis. Fourier analysis --- Mathematics --- Mathematical physics --- Computer. Automation --- beeldverwerking --- Fourieranalyse --- toegepaste wiskunde --- wiskunde --- signaalverwerking