Inequalities from Complex Analysis

John P. D'Angelo

264 pages, parution le 17/03/2003

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Résumé

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 real-valued 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.

Contents

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
Afterword
Appendix A

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	John P. D'Angelo
Parution	17/03/2003
Nb. de pages	264
Format	14,5 x 21,5
Couverture	Broché
Poids	430g
Intérieur	Noir et Blanc
EAN13	9780883850336
ISBN13	978-0-88385-033-6