The Geometry of Domains in Space PDF Download
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Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 9780817640972
Category : Mathematics
Languages : en
Pages : 324
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Book Description
"The book can be highly recommended for graduate students as a comprehensive introduction to the field of geometric analysis. Also mathematicians working in other areas can profit a lot from this carefully written book. In particular, the geometric ideas are presented in a self-contained manner; for some of the needed analytic or measure-theoretic results, references are given." -ZAA
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 9780817640972
Category : Mathematics
Languages : en
Pages : 324
Get Book Here
Book Description
"The book can be highly recommended for graduate students as a comprehensive introduction to the field of geometric analysis. Also mathematicians working in other areas can profit a lot from this carefully written book. In particular, the geometric ideas are presented in a self-contained manner; for some of the needed analytic or measure-theoretic results, references are given." -ZAA
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 1461215749
Category : Mathematics
Languages : en
Pages : 311
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Book Description
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.
Author: Robert E. Greene
Publisher: Springer Science & Business Media
ISBN: 0817646221
Category : Mathematics
Languages : en
Pages : 310
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Book Description
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.
Author: Steven G Krantz
Publisher:
ISBN: 9781461215752
Category :
Languages : en
Pages : 324
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Book Description
Author: Peter Gardenfors
Publisher: MIT Press
ISBN: 9780262572194
Category : Psychology
Languages : en
Pages : 324
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Book Description
Within cognitive science, two approaches currently dominate the problem of modeling representations. The symbolic approach views cognition as computation involving symbolic manipulation. Connectionism, a special case of associationism, models associations using artificial neuron networks. Peter Gärdenfors offers his theory of conceptual representations as a bridge between the symbolic and connectionist approaches. Symbolic representation is particularly weak at modeling concept learning, which is paramount for understanding many cognitive phenomena. Concept learning is closely tied to the notion of similarity, which is also poorly served by the symbolic approach. Gärdenfors's theory of conceptual spaces presents a framework for representing information on the conceptual level. A conceptual space is built up from geometrical structures based on a number of quality dimensions. The main applications of the theory are on the constructive side of cognitive science: as a constructive model the theory can be applied to the development of artificial systems capable of solving cognitive tasks. Gärdenfors also shows how conceptual spaces can serve as an explanatory framework for a number of empirical theories, in particular those concerning concept formation, induction, and semantics. His aim is to present a coherent research program that can be used as a basis for more detailed investigations.
Author: Pertti Mattila
Publisher: Cambridge University Press
ISBN: 9780521655958
Category : Mathematics
Languages : en
Pages : 360
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Book Description
This book studies the geometric properties of general sets and measures in euclidean space.
Author: Francis Bonahon
Publisher: American Mathematical Soc.
ISBN: 082184816X
Category : Mathematics
Languages : en
Pages : 403
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Book Description
The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.
Author: Lyndon Woodward
Publisher: Cambridge University Press
ISBN: 1108424937
Category : Mathematics
Languages : en
Pages : 275
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Book Description
With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.
Author: Peter Gärdenfors
Publisher: MIT Press
ISBN: 0262026783
Category : Language Arts & Disciplines
Languages : en
Pages : 357
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Book Description
A novel cognitive theory of semantics that proposes that the meanings of words can be described in terms of geometric structures.
Author: Mark Green
Publisher: Princeton University Press
ISBN: 1400842735
Category : Mathematics
Languages : en
Pages : 298
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Book Description
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.
