Analysis And Geometry On Complex Homogeneous Domains
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Analysis And Geometry On Complex Homogeneous Domains
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Author : Jacques Faraut
language : en
Publisher:
Release Date : 1999-12-10
Analysis And Geometry On Complex Homogeneous Domains written by Jacques Faraut and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-10 with categories.
Analysis And Geometry On Complex Homogeneous Domains
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Author : Jacques Faraut
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis And Geometry On Complex Homogeneous Domains written by Jacques Faraut and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. The most basic type of domain examined is the bounded symmetric domain, originally described and classified by Cartan and Harish- Chandra. Two of the five parts of the text deal with these domains: one introduces the subject through the theory of semisimple Lie algebras (Koranyi), and the other through Jordan algebras and triple systems (Roos). Larger classes of domains and spaces are furnished by the pseudo-Hermitian symmetric spaces and related R-spaces. These classes are covered via a study of their geometry and a presentation and classification of their Lie algebraic theory (Kaneyuki). In the fourth part of the book, the heat kernels of the symmetric spaces belonging to the classical Lie groups are determined (Lu). Explicit computations are made for each case, giving precise results and complementing the more abstract and general methods presented. Also explored are recent developments in the field, in particular, the study of complex semigroups which generalize complex tube domains and function spaces on them (Faraut). This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis, or as a self-study resource for newcomers to the field. Readers will reach the frontiers of the subject in a considerably shorter time than with existing texts.
Theory Of Complex Homogeneous Bounded Domains
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Author : Yichao Xu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31
Theory Of Complex Homogeneous Bounded Domains written by Yichao Xu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-31 with Mathematics categories.
This book is the first to systematically explore the classification and function theory of complex homogeneous bounded domains. The Siegel domains are discussed in detail, and proofs are presented. Using the normal Siegel domains to realize the homogeneous bounded domains, we can obtain more property of the geometry and the function theory on homogeneous bounded domains.
Geometric Analysis And Applications To Quantum Field Theory
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Author : Peter Bouwknegt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Analysis And Applications To Quantum Field Theory written by Peter Bouwknegt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.
Complex Convexity And Analytic Functionals
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Author : Mats Andersson
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Complex Convexity And Analytic Functionals written by Mats Andersson and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A set in complex Euclidean space is called C-convex if all its intersections with complex lines are contractible, and it is said to be linearly convex if its complement is a union of complex hyperplanes. These notions are intermediates between ordinary geometric convexity and pseudoconvexity. Their importance was first manifested in the pioneering work of André Martineau from about forty years ago. Since then a large number of new related results have been obtained by many different mathematicians. The present book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappié transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.
Rigid Analytic Geometry And Its Applications
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Author : Jean Fresnel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Rigid Analytic Geometry And Its Applications written by Jean Fresnel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.
Number Fields And Function Fields Two Parallel Worlds
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Author : Gerard van der Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-09-14
Number Fields And Function Fields Two Parallel Worlds written by Gerard van der Geer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-14 with Mathematics categories.
Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections
Contributions To Complex Analysis And Analytic Geometry
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Author : Henri Skoda
language : en
Publisher: Springer-Verlag
Release Date : 2013-08-13
Contributions To Complex Analysis And Analytic Geometry written by Henri Skoda and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.
Combinatorial Algebraic Geometry
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Author : Aldo Conca
language : en
Publisher: Springer
Release Date : 2014-05-15
Combinatorial Algebraic Geometry written by Aldo Conca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-15 with Mathematics categories.
Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions and enumerative geometry. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varieties endowed with a rich combinatorial structure. Relevant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications.
Jordan Triple Systems In Complex And Functional Analysis
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Author : José M. Isidro
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-09
Jordan Triple Systems In Complex And Functional Analysis written by José M. Isidro and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-09 with Education categories.
This book is a systematic account of the impressive developments in the theory of symmetric manifolds achieved over the past 50 years. It contains detailed and friendly, but rigorous, proofs of the key results in the theory. Milestones are the study of the group of holomomorphic automorphisms of bounded domains in a complex Banach space (Vigué and Upmeier in the late 1970s), Kaup's theorem on the equivalence of the categories of symmetric Banach manifolds and that of hermitian Jordan triple systems, and the culminating point in the process: the Riemann mapping theorem for complex Banach spaces (Kaup, 1982). This led to the introduction of wide classes of Banach spaces known as JB∗-triples and JBW∗-triples whose geometry has been thoroughly studied by several outstanding mathematicians in the late 1980s. The book presents a good example of fruitful interaction between different branches of mathematics, making it attractive for mathematicians interested in various fields such as algebra, differential geometry and, of course, complex and functional analysis.