Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry (Cornerstones)

__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.​ 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. 1. Introduction To Fourier Series -- 2. Hilbert Spaces -- 3. Fourier Transform On R -- 4. Geometric Considerations -- 5. Appendix. John P. D'angelo. Includes Bibliographical References And Index. ​​ 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.​ Front Matter....Pages i-x Introduction to Fourier Series....Pages 1-43 Hilbert Spaces....Pages 45-94 Fourier Transform on R....Pages 95-119 Geometric Considerations....Pages 121-178 Appendix....Pages 179-192 Back Matter....Pages 193-203