More Explorations in Complex Functions

Richard Beals is Professor Emeritus of Mathematics at Yale University. His research interests include ordinary and partial differential equations, operator theory, integrable systems, and transport theory. He has authored many books, including Advanced Mathematical Analysis, published in 1973 as the twelfth volume in the series Graduate Texts in Mathematics.Roderick S. C. Wong is Professor Emeritus of Mathematics at the City University of Hong Kong. His research interests include asymptotic analysis, perturbation methods, and special functions. He has been president of the Canadian Applied Mathematics Society and the Hong Kong Mathematical Society, and received numerous professional honors, including election to the European Academy of Sciences in 2007. He has written and edited a wide variety of books, with several notable works in the area of special functions.

“This book covers a variety of topics in the area of complex analysis. … The text contains a nice diagram … . Every chapter includes a literature review … . the sheer scope of the text makes it an excellent source of advanced topics suitable for a graduate-level course.” (James Tipton, Mathematical Reviews, January, 2025) “The material is presented very well ... . The book is excellent as a quick introduction to an outsider to any of the topics included in the book, or as supplementary reading for a topics based second course in complex analysis.” (Amol Sasane, zbMATH 1529.30001, 2024)

• 1. Basics.- 2. Further preliminaries.- 3. Complex dynamics.- 4. Univalent functions and de Brange's theorem.- 5. Harmonic and subharmonic functions; the Dirichlet problem.- 6. General Riemann surfaces.- 7. The uniformization theorem.- 8. Quasiconformal mapping.- 9. Introduction to Teichmüller theory.- 10. The Bergman kernel.- 11. Theta functions.- 12. Padé approximants and continued fractions.- 13. Riemann–Hilbert problems.- 14. Asymptotic and Darboux's method.- References.- Index.