TY  - BOOK
AU  - Krantz,Steven G.
ED  - SpringerLink (Online service)
TI  - Geometric Analysis of the Bergman Kernel and Metric
T2  - Graduate Texts in Mathematics,
SN  - 9781461479246
AV  - QA299.6-433 
U1  - 515 23
PY  - 2013///
CY  - New York, NY
PB  - Springer New York, Imprint: Springer
KW  - Mathematics
KW  - Mathematical analysis
KW  - Analysis (Mathematics)
KW  - Functional analysis
KW  - Partial differential equations
KW  - Differential geometry
KW  - Analysis
KW  - Partial Differential Equations
KW  - Functional Analysis
KW  - Differential Geometry
N1  - Preface -- 1. Introductory Ideas -- 2. The Bergman Metric -- 3. Geometric and Analytic Ideas -- 4. Partial Differential Equations -- 5. Further Geometric Explorations -- 6. Additional Analytic Topics -- 7. Curvature of the Bergman Metric -- 8. Concluding Remarks -- Table of Notation -- Bibliography -- Index
N2  - This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory
UR  - http://dx.doi.org/10.1007/978-1-4614-7924-6
ER  -