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Birkhäuser

Hermitian Analysis

From Fourier Series to Cauchy-Riemann Geometry

  • Textbook
  • © 2013

Overview

Authors:
  1. John P. D'Angelo

    1. Department of Mathematics, University of Illinois, Urbana-Champaign, Urbana, USA

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  • Many examples and hundreds of exercises are provided to promote understanding
  • Uses the concept of orthogonality to unify various mathematical topics
  • Includes accessible content designed to lead students from undergraduate- to research-level mathematics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Cornerstones (COR)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction to Fourier Series

    • John P. D’Angelo
    Pages 1-43

  3. Hilbert Spaces

    • John P. D’Angelo
    Pages 45-94

  4. Fourier Transform on R

    • John P. D’Angelo
    Pages 95-119

  5. Geometric Considerations

    • John P. D’Angelo
    Pages 121-178

  6. Appendix

    • John P. D’Angelo
    Pages 179-192

  7. Back Matter

    Pages 193-203
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Keywords

About this book

​​Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several complex variables, and includes some of the author's results. The concept of orthogonality weaves the material into a coherent whole. This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathematics, graduate students interested in analysis, and researchers interested in some basic aspects of CR Geometry. The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class.​

Reviews

From the book reviews:

“The present book developed from the teaching experiences of the author in several honors courses. … All the topics are motivated very nicely, and there are many exercises, which make the book ideal for a first-year graduate course on the subject. … The style is concise, always very neat, and proofs are given with full details. Hence, I certainly suggest this nice textbook to anyone interested in the subject, even for self-study.” (Fabio Nicola, Mathematical Reviews, July, 2014)

“This is a clearly written and attractive textbook using a new concept. … The book includes numerous examples and more than 270 exercises. … I warmly recommend this book to all graduate students.” (László Leindler, zbMATH, Vol. 1281, 2014)

Authors and Affiliations

  • Department of Mathematics, University of Illinois, Urbana-Champaign, Urbana, USA

    John P. D'Angelo

Bibliographic Information

  • Book Title: Hermitian Analysis

  • Book Subtitle: From Fourier Series to Cauchy-Riemann Geometry

  • Authors: John P. D'Angelo

  • Series Title: Cornerstones

  • DOI: https://doi.org/10.1007/978-1-4614-8526-1

  • Publisher: Birkhäuser New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media New York 2013

  • Softcover ISBN: 978-1-4939-4898-7Published: 23 August 2016

  • eBook ISBN: 978-1-4614-8526-1Published: 24 September 2013

  • Series ISSN: 2197-182X

  • Series E-ISSN: 2197-1838

  • Edition Number: 1

  • Number of Pages: X, 203

  • Number of Illustrations: 8 b/w illustrations, 19 illustrations in colour

  • Topics: Fourier Analysis, Differential Geometry, Ordinary Differential Equations

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