Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry

ISBN-13: 9781493948987 / Angielski / Miękka / 2016 / 203 str.

John P. D'Angelo

Opis

​​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.​

Recenzje

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)

Spis treści

​ ​Preface.- Introduction to Fourier series.- Hilbert spaces.- Fourier transform on R.- Geometric considerations.- Appendix.- References.- Index. 

Blurb

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.