Hardcover ISBN:  9780883850336 
Product Code:  CAR/28 
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AMS Member Price:  $37.50 
eBook ISBN:  9780883859704 
Product Code:  CAR/28.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
Hardcover ISBN:  9780883850336 
eBook: ISBN:  9780883859704 
Product Code:  CAR/28.B 
List Price:  $95.00 $72.50 
MAA Member Price:  $71.25 $54.38 
AMS Member Price:  $71.25 $54.38 
Hardcover ISBN:  9780883850336 
Product Code:  CAR/28 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
eBook ISBN:  9780883859704 
Product Code:  CAR/28.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
Hardcover ISBN:  9780883850336 
eBook ISBN:  9780883859704 
Product Code:  CAR/28.B 
List Price:  $95.00 $72.50 
MAA Member Price:  $71.25 $54.38 
AMS Member Price:  $71.25 $54.38 

Book DetailsThe Carus Mathematical MonographsVolume: 28; 2002; 264 pp
Inequalities from Complex Analysis is a careful, friendly exposition of inequalities and positivity conditions for various mathematical objects arising in complex analysis. The author begins by defining the complex number field, and then discusses enough mathematical analysis to reach recently published research on positivity conditions for functions of several complex variables. The development culminates in complete proofs of a stabilization theorem relating two natural positivity conditions for realvalued polynomials of several complex variables. The reader will also encounter the Bergman kernel function, Fourier series, Hermitian linear algebra, the spectral theorem for compact Hermitian operators, plurisubharmonic functions, and some delightful inequalities. Numerous examples, exercises, and discussions of geometric reasoning appear along the way.
Undergraduate mathematics majors who have seen elementary real analysis can easily read the first five chapters of this book, and second year graduate students in mathematics can read the entire text. Some physicists and engineers may also find the topics and discussions useful. The inequalities and positivity conditions herein form the foundation for a small but beautiful part of complex analysis.

Table of Contents

Chapters

Chapter I. Complex Numbers

Chapter II. Complex Euclidean Spaces and Hilbert Spaces

Chapter III. Complex Analysis in Several Variables

Chapter IV. Linear Transformations and Positivity Conditions

Chapter V. Compact and Integral Operators

Chapter VI. Positivity Conditions for Realvalued Functions

Chapter VII. Stabilization and Applications

Chapter VIII. Afterword


Additional Material

Reviews

The book is nicely organized and well written for readers who have a background in real analysis and complex variable theory. The book is carefully prepared ... It will be a valuable resource for research libraries.
Richard Chechile, Journal of Mathematical Psychology 
I really enjoyed reading this book. ... The first five chapters are accessible to the broad mathematical community with basic training in analysis and are useful for an honors course at the senior undergraduate level. The entire book offers an attractive but demanding introduction to modern complex analysis at the graduate level.
Jeffrey Nunemacher, MAA Online 
This short book takes readers from the first properties of the complex numbers, all the way to current research. On the way, the readers will acquire essential tools from complex analysis, linear algebra, Hilbert space, several complex variables, Fourier analysis, and operator theory. Even more remarkably, the pace seems leisurely, with many delightful digressions, some nearly as interesting as the main results. ... such a book affords the undergraduate the pleasant opportunity to learn important basics by immediately seeing them fit together into something of beauty.
D. V. Felman, CHOICE


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Inequalities from Complex Analysis is a careful, friendly exposition of inequalities and positivity conditions for various mathematical objects arising in complex analysis. The author begins by defining the complex number field, and then discusses enough mathematical analysis to reach recently published research on positivity conditions for functions of several complex variables. The development culminates in complete proofs of a stabilization theorem relating two natural positivity conditions for realvalued polynomials of several complex variables. The reader will also encounter the Bergman kernel function, Fourier series, Hermitian linear algebra, the spectral theorem for compact Hermitian operators, plurisubharmonic functions, and some delightful inequalities. Numerous examples, exercises, and discussions of geometric reasoning appear along the way.
Undergraduate mathematics majors who have seen elementary real analysis can easily read the first five chapters of this book, and second year graduate students in mathematics can read the entire text. Some physicists and engineers may also find the topics and discussions useful. The inequalities and positivity conditions herein form the foundation for a small but beautiful part of complex analysis.

Chapters

Chapter I. Complex Numbers

Chapter II. Complex Euclidean Spaces and Hilbert Spaces

Chapter III. Complex Analysis in Several Variables

Chapter IV. Linear Transformations and Positivity Conditions

Chapter V. Compact and Integral Operators

Chapter VI. Positivity Conditions for Realvalued Functions

Chapter VII. Stabilization and Applications

Chapter VIII. Afterword

The book is nicely organized and well written for readers who have a background in real analysis and complex variable theory. The book is carefully prepared ... It will be a valuable resource for research libraries.
Richard Chechile, Journal of Mathematical Psychology 
I really enjoyed reading this book. ... The first five chapters are accessible to the broad mathematical community with basic training in analysis and are useful for an honors course at the senior undergraduate level. The entire book offers an attractive but demanding introduction to modern complex analysis at the graduate level.
Jeffrey Nunemacher, MAA Online 
This short book takes readers from the first properties of the complex numbers, all the way to current research. On the way, the readers will acquire essential tools from complex analysis, linear algebra, Hilbert space, several complex variables, Fourier analysis, and operator theory. Even more remarkably, the pace seems leisurely, with many delightful digressions, some nearly as interesting as the main results. ... such a book affords the undergraduate the pleasant opportunity to learn important basics by immediately seeing them fit together into something of beauty.
D. V. Felman, CHOICE