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000746151 019__ $$a923335802
000746151 020__ $$a9784431557470$$qelectronic book
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000746151 020__ $$z9784431557463
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000746151 0247_ $$a10.1007/978-4-431-55747-0$$2doi
000746151 035__ $$aSP(OCoLC)ocn922581436
000746151 035__ $$aSP(OCoLC)922581436$$z(OCoLC)923335802
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000746151 1001_ $$aŌsawa, Takeo,$$d1951-$$eauthor.
000746151 24510 $$aL2 approaches in several complex variables$$h[electronic resource] :$$bdevelopment of Oka-Cartan Theory by L2 estimates for the ? ̄operator /$$cTakeo Ōsawa.
000746151 264_1 $$aTokyo :$$bSpringer,$$c2015.
000746151 300__ $$a1 online resource (196 pages)
000746151 336__ $$atext$$btxt$$2rdacontent
000746151 337__ $$acomputer$$bc$$2rdamedia
000746151 338__ $$aonline resource$$bcr$$2rdacarrier
000746151 4901_ $$aSpringer monographs in mathematics
000746151 504__ $$aIncludes bibliographical references.
000746151 5050_ $$aPart I Holomorphic Functions and Complex Spaces -- Convexity Notions -- Complex Manifolds -- Classical Questions of Several Complex Variables -- Part II The Method of L² Estimates -- Basics of Hilb ert Space Theory -- Harmonic Forms -- Vanishing Theorems -- Finiteness Theorems -- Notes on Complete Kahler Domains (= CKDs) -- Part III L² Variant of Oka-Cartan Theory -- Extension Theorems -- Division Theorems -- Multiplier Ideals -- Part IV Bergman Kernels -- The Bergman Kernel and Metric -- Bergman Spaces and Associated Kernels -- Sequences of Bergman Kernels -- Parameter Dependence -- Part V L² Approaches to Holomorphic Foliations -- Holomorphic Foliation and Stable Sets -- L² Method Applied to Levi Flat Hypersurfaces -- LFHs in Tori and Hopf Surfaces.
000746151 506__ $$aAccess limited to authorized users.
000746151 520__ $$aThe purpose of this monograph is to present the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Highlighted are the new precise results on the L² extension of holomorphic functions. In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the L² method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka-Cartan theory is given by this method. The L² extension theorem with an optimal constant is included, obtained recently by Z. Błocki and by Q.-A. Guan and X.-Y. Zhou separately. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani-Yamaguchi, Berndtsson, and Guan-Zhou. Most of these results are obtained by the L² method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the L² method obtained during these 15 years.
000746151 588__ $$aDescription based on print version record.
000746151 650_0 $$aFunctions of several complex variables.
000746151 77608 $$iPrint version:$$aŌsawa, Takeo, 1951- author.$$tL2 approaches in several complex variables$$z9784431557463$$w(OCoLC)921827580
000746151 830_0 $$aSpringer monographs in mathematics.
000746151 85280 $$bebk$$hSpringerLink
000746151 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-4-431-55747-0$$zOnline Access$$91397441.1
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