Inequalities from Complex Analysis (Carus Mathematical Monographs, Series Number 28) by John P. D’Angelo (PDF)

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Inequalities from Complex Analysis is a careful, friendly exposition of some rather interesting mathematics. The author begins by defining the complex number field; he gives a novel presentation of some standard mathematical analysis in the early chapters. The development culminates with some results from recent research literature. The book provides complete yet comprehensible proofs as well as some surprising consequences of the results. One unifying theme is a complex variables analogue of Hilbert’s seventeenth problem. Numerous examples, exercises and discussions of geometric reasoning aid the reader. The book is accessible to undergraduate mathematicians, as well as physicists and engineers.

User’s Reviews

Editorial Reviews: Review The reader is rewarded with lively prose, sparkling examples, and elucidating exercises. –Steven Krantz, Washington University, St. Louis Book Description Inequalities from complex analysis. Theory, examples and applications. About the Author John P. D’Angelo received his PhD form Princeton University in 1976, and has been at the University of Illinois in Urbana since 1978. He has held visiting positions at Princeton University, Washington University in St. Louis, the Institute for Advanced Study in Princeton, the Mathematical Sciences Research Institute in Berkeley, and the Mittag-Leftler Institute in Sweden. He has often been named to the “Incomplete List of Professors Ranked Excellent by their Students at Illinois.” He was the 1999 winner of the Bergman Prize, and has been cited for several important contributions to complex analysis, including his work on degenerate Levi forms and points of finite type, as well as work––some joint with David Catlin––on positivity conditions in complex analysis. Read more

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