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Über dieses Buch

​​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.​

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction to Fourier Series

Abstract
The first chapter discusses Fourier series and differential equations.
John P. D’Angelo

Chapter 2. Hilbert Spaces

Abstract
The second chapter discusses linear operators on Hilbert spaces, with applications to Fourier series and special functions.
John P. D’Angelo

Chapter 3. Fourier Transform on R

Abstract
We define and study the Fourier transform in this chapter. Rather than working with functions defined on the circle, we consider functions defined on the real line R. Among many books, the reader can consult [E, G] and [GS] for applications of Fourier transforms to applied mathematics, physics, and engineering. See [F1] for an advanced mathematical treatment.
John P. D’Angelo

Chapter 4. Geometric Considerations

Abstract
The fourth chapter discusses geometric problems in several complex variables.
John P. D’Angelo

Chapter 5. Appendix

Abstract
The fifth chapter is an appendix reviewing the prerequisites for the course: the real and complex number systems, metric spaces, complex analytic functions, probability.
John P. D’Angelo

Backmatter

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