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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

- Series:
**Graduate Texts in Mathematics 250** - Author:
**Loukas Grafakos (auth.)** - Year:
**2009** - Publisher:
**Springer New York** - Language:
**English** - ISBN:
**0387094334,9780387094335**

- File size:
**3 060 727** - Format:
**pdf**

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Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by CalderĂłn and Zygmund. The text was born from a graduate course taught at the Universidad AutĂłnoma de Ma...

This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of genera...

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourie...

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to moti...

A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acq...

Discover applications of Fourier analysis on finite non-Abelian groupsThe majority of publications in spectral techniques consider Fourier transform on Abelian groups. However, non-Abelian groups provide notable advantages in efficient implementations of ...

Written by a successful author and respected mathematician, this book emphasizes a concrete and computational approach to the subject of Fourier analysis and wavelet theory while maintaining a balance between theory and applications. In some cases, severa...

A paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolute continuity on differentiati...

CIRCUIT ANALYSIS: THEORY AND PRACTICE, Fifth Edition, provides a thorough, engaging introduction to the theory, design, and analysis of electrical circuits. Comprehensive without being overwhelming, this reader-friendly book combines a detailed exploratio...

Moderne Verfahren der Nachrichtenanalyse werden praxisorientiert beschrieben. Notation und Darstellung entsprechen den Gewohnheiten der Ingenieure. Den praktischen Nutzen der lĂ¶sungsorientierten Darstellungsform unterstreicht der Verzicht auf umfassende H...

This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economi...

When did life first appear on Earth and what form did it take? The answer to this intriguing and fundamentally important question lies somewhere within the early Archean rock record. The young Earth was, however, a very different place to that we know tod...

Life on Earth: An Encyclopedia of Biodiversity, Ecology, and Evolution tackles the critical issue for humanity in the 21st centuryĂ˘â‚¬â€ťour ever more menacing impact on the environment. This two-volume, illustrated set, edited by American Museum of Natural...

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