The Geometry Of Domains In Space
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The Geometry Of Domains In Space
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Geometry Of Domains In Space written by Steven G. Krantz 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.
The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the Fourier transform. Pseudodifferential operators and Fourier integral operators can playa role in solving some of the problems, but other problems require new, more geometric, ideas. At a more basic level, the analysis of a smoothly bounded domain in space requires a great deal of preliminary spadework. Tubular neighbor hoods, the second fundamental form, the notion of "positive reach", and the implicit function theorem are just some of the tools that need to be invoked regularly to set up this analysis. The normal and tangent bundles become part of the language of classical analysis when that analysis is done on a domain. Many of the ideas in partial differential equations-such as Egorov's canonical transformation theorem-become rather natural when viewed in geometric language. Many of the questions that are natural to an analyst-such as extension theorems for various classes of functions-are most naturally formulated using ideas from geometry.
The Geometry Of Domains In Space
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Author : Steven G Krantz
language : en
Publisher:
Release Date : 1999-05-01
The Geometry Of Domains In Space written by Steven G Krantz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-01 with categories.
Nonlinear Semigroups Fixed Points And Geometry Of Domains In Banach Spaces
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Author : Simeon Reich
language : en
Publisher: Imperial College Press
Release Date : 2005
Nonlinear Semigroups Fixed Points And Geometry Of Domains In Banach Spaces written by Simeon Reich and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces. Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments. Contents: Mappings in Metric and Normed Spaces; Differentiable and Holomorphic Mappings in Banach Spaces; Hyperbolic Metrics on Domains in Complex Banach Spaces; Some Fixed Point Principles; The DenjoyOCoWolff Fixed Point Theory; Generation Theory for One-Parameter Semigroups; Flow-Invariance Conditions; Stationary Points of Continuous Semigroups; Asymptotic Behavior of Continuous Flows; Geometry of Domains in Banach Spaces."
The Geometry Of Complex Domains
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Author : Robert E. Greene
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-18
The Geometry Of Complex Domains written by Robert E. Greene 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 2011-05-18 with Mathematics categories.
This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space. At once authoritative and accessible, this text touches upon many important parts of modern mathematics: complex geometry, equivalent embeddings, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces. The Geometry of Complex Domains can serve as a “coming of age” book for a graduate student who has completed at least one semester or more of complex analysis, and will be most welcomed by analysts and geometers engaged in current research.
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.
Automorphic Functions And The Geometry Of Classical Domains
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Author : Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro
language : en
Publisher: Routledge
Release Date : 1969
Automorphic Functions And The Geometry Of Classical Domains written by Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
New Trends In Geometry
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Author : Claudio Bartocci
language : en
Publisher: World Scientific
Release Date : 2011-05-19
New Trends In Geometry written by Claudio Bartocci and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-19 with Mathematics categories.
This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines. The integration of mathematics with physics, as well as molecular and cell biology and the neurosciences, will constitute the new frontier of 21st century science, where breakthroughs are more likely to span across traditional disciplines. Contents:Geometry, Theoretical Physics and Cosmology:The Emergence of Algebraic Geometry in Contemporary Physics (Claudio Bartocci & Ugo Bruzzo)Quantum Gravity and Quantum Geometry (Mauro Carfora)The de Sitter and Anti-de Sitter Universes (Ugo Moschella)Geometry and Topology in Relativistic Cosmology (Jean-Pierre Luminet)The Problem of Space in Neurosciences:Space Coding in the Cerebral Cortex (Leonardo Fogassi)Action and Space Representation (Anna Berti & Alessia Folegatti)The Space Representations in the Brain (Claudio Brozzoli & Alessandro Farnè)The Enactive Constitution of Space (Carrado Sinigaglia & Chiara Brozzo)Geometrical Methods in the Biological Sciences:Causes and Symmetries in Natural Sciences: The Continuum and the Discrete in Mathematical Modelling (Francis Bailly & Giuseppe Longo)Topological Invariants of Geometrical Surfaces and the Protein Folding Problem (Riccardo Broglia)The Geometry of Dense Packing and Biological Structures (Jean-François Sadoc)When Topology and Biology Meet ‘For Life’: The Interactions Between Topological Forms and Biological Functions (Luciano Boi) Readership: Students and researchers in mathematical sciences at graduate level. Keywords:Geometrical Models;Spatial Perception;Mirror Neurons;Quantum Field Theory;String TheoryKey Features:Multidisciplinary approachDistinguished contributors working in different research areasNovel perspectives on the interactions between mathematics and biology
Offbeat Integral Geometry On Symmetric Spaces
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Author : Valery V. Volchkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-30
Offbeat Integral Geometry On Symmetric Spaces written by Valery V. Volchkov 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 2013-01-30 with Mathematics categories.
The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory.
Analytic Geometry Of Space
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Author : Virgil Snyder
language : en
Publisher:
Release Date : 1914
Analytic Geometry Of Space written by Virgil Snyder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1914 with Geometry, Analytic categories.
Geometric Analysis And Function Spaces
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Author : Steven George Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-01-01
Geometric Analysis And Function Spaces written by Steven George Krantz 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 1993-01-01 with Mathematics categories.
This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.