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001 978-1-4614-7924-6
003 DE-He213
005 20140220082830.0
007 cr nn 008mamaa
008 130920s2013 xxu| s |||| 0|eng d
020 _a9781461479246
_9978-1-4614-7924-6
024 7 _a10.1007/978-1-4614-7924-6
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aKrantz, Steven G.
_eauthor.
245 1 0 _aGeometric Analysis of the Bergman Kernel and Metric
_h[electronic resource] /
_cby Steven G. Krantz.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXIII, 292 p. 7 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v268
505 0 _aPreface -- 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.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aFunctional analysis.
650 0 _aDifferential equations, partial.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aPartial Differential Equations.
650 2 4 _aFunctional Analysis.
650 2 4 _aDifferential Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461479239
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v268
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-7924-6
912 _aZDB-2-SMA
999 _c96005
_d96005