Hermitian Analysis

From Fourier Series to Cauchy-Riemann Geometry

  • John P. D'Angelo

Part of the Cornerstones book series (COR)

Table of contents

  1. Front Matter
    Pages i-x
  2. John P. D’Angelo
    Pages 1-43
  3. John P. D’Angelo
    Pages 45-94
  4. John P. D’Angelo
    Pages 95-119
  5. John P. D’Angelo
    Pages 121-178
  6. John P. D’Angelo
    Pages 179-192
  7. Back Matter
    Pages 193-203

About this book

Introduction

Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from 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 in several complex variables. The final chapter includes complex differential forms, geometric inequalities from one and several complex variables, finite unitary groups, proper mappings, and naturally leads to the Cauchy-Riemann geometry of the unit sphere. The book thus takes the reader from the unit circle to the unit sphere.

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. It will also be useful for students in physics and engineering, as it includes topics in harmonic analysis arising in these subjects. The inclusion of an appendix and more than 270 exercises makes this book suitable for a capstone undergraduate Honors class.

Keywords

Complex differential forms Fourier series Geometric inequalities Hilbert spaces

Authors and affiliations

  • John P. D'Angelo
    • 1
  1. 1.Department of MathematicsUniversity of Illinois, Urbana-ChampaignUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-8526-1
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-8525-4
  • Online ISBN 978-1-4614-8526-1
  • Series Print ISSN 2197-182X
  • Series Online ISSN 2197-1838
  • About this book
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