This integrated book begins by discussing Fourier series, Hilbert spaces and the Fourier transform on the real line, and then turns to the heart of the text, geometric considerations. The concept of orthogonality weaves the material into a coherent whole.

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.

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

Autorentext

John P. D'Angelo, PhD, is a Professor in the Department of Mathematics at the University of Illiniois at Urbana-Champaign, USA

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