TY - BOOK ID - 7912542 TI - Geometric Analysis of the Bergman Kernel and Metric PY - 2013 SN - 1461479231 146147924X PB - New York, NY : Springer New York : Imprint: Springer, DB - UniCat KW - Bergman kernel functions KW - Engineering & Applied Sciences KW - Applied Mathematics KW - Kernel functions, Bergman 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. KW - Global analysis (Mathematics). KW - Differential equations, partial. KW - Global differential geometry. KW - Geometry, Differential KW - Partial differential equations KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Bergman kernel functions. KW - Differential geometry KW - 517.1 Mathematical analysis KW - Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:7912542 AB - 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. ER -