# Hermitian Analysis

## From Fourier Series to Cauchy-Riemann Geometry

• John P. D'Angelo
Book

Part of the Cornerstones book series (COR)

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

### 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