Geometric Analysis And Function Spaces

Author : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 46,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821807347

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Geometric Analysis and Function Spaces by Steven George Krantz Pdf

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.

Author : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 40,5 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0821889257

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Geometric Analysis and Function Spaces by Steven George Krantz Pdf

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.

Author : R. B. Holmes
Publisher : Springer
Page : 0 pages
File Size : 44,5 Mb
Release : 2012-12-12
Category : Mathematics
ISBN : 146849371X

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Geometric Functional Analysis and its Applications by R. B. Holmes Pdf

This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its appli cations. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the Hahn Banach principle, the latter appearing in ten different but equivalent formula tions (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces.

Author : Keith M. Ball,Vitali Milman
Publisher : Cambridge University Press
Page : 260 pages
File Size : 54,7 Mb
Release : 1999-01-28
Category : Mathematics
ISBN : 0521642590

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Convex Geometric Analysis by Keith M. Ball,Vitali Milman Pdf

Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999.

Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
Page : 693 pages
File Size : 44,8 Mb
Release : 2000
Category : Geometry, Differential
ISBN : 9780821826737

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Groups and Geometric Analysis by Sigurdur Helgason Pdf

This volume, the second of Helgason's impressive three books on Lie groups and the geometry and analysis of symmetric spaces, is an introduction to group-theoretic methods in analysis on spaces with a group action. The first chapter deals with the three two-dimensional spaces of constant curvature, requiring only elementary methods and no Lie theory. It is remarkably accessible and would be suitable for a first-year graduate course. The remainder of the book covers more advanced topics, including the work of Harish-Chandra and others, but especially that of Helgason himself. Indeed, the exposition can be seen as an account of the author's tremendous contributions to the subject.Chapter I deals with modern integral geometry and Radon transforms. The second chapter examines the interconnection between Lie groups and differential operators. Chapter IV develops the theory of spherical functions on semisimple Lie groups with a certain degree of completeness, including a study of Harish-Chandra's $c$-function. The treatment of analysis on compact symmetric spaces (Chapter V) includes some finite-dimensional representation theory for compact Lie groups and Fourier analysis on compact groups. Each chapter ends with exercises (with solutions given at the end of the book!) and historical notes.This book, which is new to the AMS publishing program, is an excellent example of the author's well-known clear and careful writing style. It has become the standard text for the study of spherical functions and invariant differential operators on symmetric spaces. Sigurdur Helgason was awarded the Steele Prize for Groups and Geometric Analysis and the companion volume, ""Differential Geometry, Lie Groups and Symmetric Spaces.""

Author : Steven G. Krantz,Harold R. Parks
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215745

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The Geometry of Domains in Space by Steven G. Krantz,Harold R. Parks Pdf

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 : Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman
Publisher : American Mathematical Society
Page : 645 pages
File Size : 41,5 Mb
Release : 2021-12-13
Category : Mathematics
ISBN : 9781470463601

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Asymptotic Geometric Analysis, Part II by Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman Pdf

This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series. Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families. Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities.

Author : Phillip Griffiths,Sigurdur Helgason
Publisher : American Mathematical Society(RI)
Page : 657 pages
File Size : 46,5 Mb
Release : 2008
Category : Electronic books
ISBN : 1470412667

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Geometric Analysis on Symmetric Spaces by Phillip Griffiths,Sigurdur Helgason Pdf

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 938 pages
File Size : 51,5 Mb
Release : 2023-03-03
Category : Mathematics
ISBN : 9783031137181

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Geometric Harmonic Analysis II by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

This monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. Volume II is concerned with function spaces measuring size and/or smoothness, such as Hardy spaces, Besov spaces, Triebel-Lizorkin spaces, Sobolev spaces, Morrey spaces, Morrey-Campanato spaces, spaces of functions of Bounded Mean Oscillations, etc., in general geometric settings. Work here also highlights the close interplay between differentiability properties of functions and singular integral operators. The text is intended for researchers, graduate students, and industry professionals interested in harmonic analysis, functional analysis, geometric measure theory, and function space theory.

Author : Bo'az Klartag,Shahar Mendelson,Vitali D. Milman
Publisher : Springer
Page : 444 pages
File Size : 44,6 Mb
Release : 2012-07-25
Category : Mathematics
ISBN : 9783642298493

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Geometric Aspects of Functional Analysis by Bo'az Klartag,Shahar Mendelson,Vitali D. Milman Pdf

This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the general trends of Asymptotic Geometric Analysis, understood in a broad sense, and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convex bodies, inequalities involving volumes of such bodies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensional spaces and characterization of classical constructions in Geometry and Analysis (like the Legendre and Fourier transforms, derivation and others). All the papers here are original research papers.

Author : Alexander Brudnyi,Prof. Yuri Brudnyi Technion R&D Foundation Ltd
Publisher : Springer Science & Business Media
Page : 577 pages
File Size : 42,7 Mb
Release : 2011-10-07
Category : Mathematics
ISBN : 9783034802093

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Methods of Geometric Analysis in Extension and Trace Problems by Alexander Brudnyi,Prof. Yuri Brudnyi Technion R&D Foundation Ltd Pdf

The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.

Author : Jie Xiao
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 40,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783764377632

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Geometric Qp Functions by Jie Xiao Pdf

This book documents the rich structure of the holomorphic Q function spaces which are geometric in the sense that they transform naturally under conformal mappings, with particular emphasis on recent development based on interaction between geometric function and measure theory and other branches of mathematical analysis, including potential theory, harmonic analysis, functional analysis, and operator theory. Largely self-contained, the book functions as an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces. Self-contained, the book functions as an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces.

Author : Monika Ludwig,Vitali D. Milman,Vladimir Pestov,Nicole Tomczak-Jaegermann
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 43,9 Mb
Release : 2013-03-27
Category : Mathematics
ISBN : 9781461464068

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Asymptotic Geometric Analysis by Monika Ludwig,Vitali D. Milman,Vladimir Pestov,Nicole Tomczak-Jaegermann Pdf

Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in the Fall of 2010 continued an established tradition of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces * Concentration of measure and isoperimetric inequalities, optimal transportation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Random matrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working in a wide range of mathematical sciences—in particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science.

Author : Iva Stavrov
Publisher : American Mathematical Soc.
Page : 243 pages
File Size : 52,9 Mb
Release : 2020-11-12
Category : Education
ISBN : 9781470456283

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Curvature of Space and Time, with an Introduction to Geometric Analysis by Iva Stavrov Pdf

This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.

Author : Sigurdur Helgason
Publisher : Unknown
Page : 637 pages
File Size : 44,8 Mb
Release : 2008
Category : Electronic
ISBN : 0821868950

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Geometric Analysis on Symmetric Spaces by Sigurdur Helgason Pdf