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Fourier Analysis

Volume 1. Theory

Part of London Mathematical Society Student Texts

  • Date Published: May 2016
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781316670965

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About the Authors
  • Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course textbook and for individual study.

    • Achieves a balance between pure and applied topics, appealing to mathematicians working in all areas
    • Includes a large number of exercises, with separate hints and solutions, to improve understanding
    • Provides an overview of topics intertwined with Fourier analysis, such as measure theory, functional analysis and complex analysis
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    Reviews & endorsements

    '[Fourier Analysis: Volume l - Theory is] fabulous … Constantin structures his exercise sets beautifully, I think: they are abundant and long, covering a spectrum of levels of difficulty; each set is followed immediately by a section of hints (in one-one correspondence); finally the hints sections are followed by very detailed and well-written solutions (also bijectively). Can there be any clearer homage to the maxim that to learn mathematics one has to get one's hands really dirty? To boot, attention to detail is ubiquitous: it's everywhere in Constantin's presentation of proofs and arguments, as well as examples, all throughout the narrative itself. The entire presentation is very much to the point and the student who works through this book will come out knowing some real mathematics very well.' Michael Berg, MAA Reviews

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    Product details

    • Date Published: May 2016
    • format: Adobe eBook Reader
    • isbn: 9781316670965
    • contains: 50 b/w illus. 200 exercises
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    1. Introduction
    2. The Lebesgue measure and integral
    3. Elements of functional analysis
    4. Convergence results for Fourier series
    5. Fourier transforms
    6. Multi-dimensional Fourier analysis
    7. A glance at some advanced topics
    Appendix: historical notes

  • Author

    Adrian Constantin, Universität Wien, Austria
    Adrian Constantin is currently Professor of Mathematics at the University of Vienna. He is an ISI Highly Cited Researcher and was invited to be plenary speaker at the 6th European Congress of Mathematics. He has received a number of international awards, including the Fluid Dynamics Research prize of the Japanese Society of Fluid Mechanics, the F. W. Bessel Research Award of the Humboldt Foundation (Germany), and the G. Gustafsson Prize of the Royal Swedish Academy of Sciences.

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