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Fourier Analysis

An Introduction
Book Hero Magic crafted this summary to help describe this book. While it's new and still learning, it may not be perfect - your feedback is welcome! Summary
Fourier Analysis by Rami Shakarchi and Elias M. Stein delves into the mathematical techniques of Fourier analysis, exploring its development and applications. The book covers fundamental concepts such as Fourier series, integrals, and transforms, while also addressing practical uses in various fields. It's a highly regarded resource for students and professionals seeking a comprehensive introduction to Fourier methods.
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Format: Hardback
$33800

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Book Hero Magic created this recommendation. While it's new and still learning, it may not be perfect - your feedback is welcome! IS THIS YOUR NEXT READ?

You might enjoy this book if you have a keen interest in mathematics and are looking to explore the fundamental concepts of Fourier analysis. The authors provide a thorough and insightful approach to the subject, offering a blend of theory and applications that may appeal to both students and professionals in the field.

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Intended for students with a beginning knowledge of mathematical analysis, this first volume, in a three-part introduction to Fourier analysis, introduces the core areas of mathematical analysis while also illustrating the organic unity between them. It includes numerous examples and applications.

Book Hero Magic formatted this description to make it easier to read. While it's new and still learning, it may not be perfect - your feedback is welcome! Description

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 Fourier arrived at in the early nineteenth century when studying problems in the physical sciencesβ€”that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution.

The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.

In organising their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering, and other sciences will find the theory and applications covered in this volume to be of real interest.

The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences.

Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions, and elements of probability theory.

Book Details

INFORMATION

ISBN: 9780691113845

Publisher: Princeton University Press

Format: Hardback

Date Published: 06 April 2003

Country: United States

Imprint: Princeton University Press

Illustration: 40 line illus.

Audience: Tertiary education, Professional and scholarly

DIMENSIONS

Width: 152.0mm

Height: 235.0mm

Weight: 595g

Pages: 328

About the Author

Elias M. Stein is Professor of Mathematics at Princeton University. Rami Shakarchi received his Ph.D. in Mathematics from Princeton University in 2002.

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