Inequalities from Complex Analysis (Carus Mathematical Monographs)

Inequalities from Complex Analysis (Carus Mathematical Monographs)
John P. D'Angelo | 1900-01-01 00:00:00 | The Mathematical Association of America | 280 | Mathematics
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.
Reviews
When I took my first course in real analysis as a graduate student, it was painfully, (literally and figuratively) obvious that success in the course was largely due to an ability to understand and manipulate inequalities. Throughout my career in mathematics since then, this opinion has been repeatedly reinforced, as I have often had to rediscover an inequality in order to solve a math problem. Knowledge of inequalities has also been a fundamental part of my work in computer science, especially in the areas of computation theory and algorithm analysis.

Therefore, I can strongly recommend this book for people who either are planning on working in complex analysis or are working in complex analysis. Many of the most widely used inequalities are explained, presented and then proved. The chapter headings are:



*) Complex numbers

*) Complex Euclidean Spaces and Hilbert Spaces

*) Complex Analysis in Several Variables

*) Linear Transformations and Positivity Conditions

*) Compact and Integral Operators

*) Positivity Conditions for Real-Valued Functions

*) Stabilization and Applications



If you are just starting out in complex analysis or need a quick refresher after some time of neglect, this is a book that will serve your needs very well.





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