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Analysis On Metric Measure Spaces
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Book Synopsis Lectures on Analysis on Metric Spaces by : Juha Heinonen
Download or read book Lectures on Analysis on Metric Spaces written by Juha Heinonen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.
Book Synopsis Sobolev Spaces on Metric Measure Spaces by : Juha Heinonen
Download or read book Sobolev Spaces on Metric Measure Spaces written by Juha Heinonen and published by Cambridge University Press. This book was released on 2015-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
Book Synopsis New Trends on Analysis and Geometry in Metric Spaces by : Fabrice Baudoin
Download or read book New Trends on Analysis and Geometry in Metric Spaces written by Fabrice Baudoin and published by Springer Nature. This book was released on 2022-02-04 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.
Book Synopsis Metric In Measure Spaces by : James J Yeh
Download or read book Metric In Measure Spaces written by James J Yeh and published by World Scientific. This book was released on 2019-11-18 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure and metric are two fundamental concepts in measuring the size of a mathematical object. Yet there has been no systematic investigation of this relation. The book closes this gap.
Book Synopsis Topics on Analysis in Metric Spaces by : Luigi Ambrosio
Download or read book Topics on Analysis in Metric Spaces written by Luigi Ambrosio and published by Oxford University Press, USA. This book was released on 2004 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the main mathematical prerequisites for analysis in metric spaces. It covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorums, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and Gromov-Hausdorff theory, all developed ina general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed on general metric spaces and as an application of the Gromov-Hausdorff theory, even in some cases when the ambient space is not locally compact. A brief and very general description of the theory of integration with respect to non-decreasing set functions is presented following the Di Giorgi method of using the 'cavalieri' formula as the definition of the integral. Based on lecture notes from Scuola Normale, this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers.
Book Synopsis Analysis and Geometry of Metric Measure Spaces by : Galia Devora Dafni
Download or read book Analysis and Geometry of Metric Measure Spaces written by Galia Devora Dafni and published by American Mathematical Soc.. This book was released on 2013 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieure in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation.
Book Synopsis Sobolev Spaces on Metric Measure Spaces by : Juha Heinonen
Download or read book Sobolev Spaces on Metric Measure Spaces written by Juha Heinonen and published by Cambridge University Press. This book was released on 2015-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincaré inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincaré inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincaré inequalities under Gromov–Hausdorff convergence, and the Keith–Zhong self-improvement theorem for Poincaré inequalities.
Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Book Synopsis Analysis on Metric-measure Spaces by : Alireza Ranjbar-Motlagh
Download or read book Analysis on Metric-measure Spaces written by Alireza Ranjbar-Motlagh and published by . This book was released on 1998 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Lipschitz Analysis by : Juha Heinonen
Download or read book Lectures on Lipschitz Analysis written by Juha Heinonen and published by . This book was released on 2005 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis On Metric-Measure Spaces: to 25; Pages:26 to 50; Pages:51 to 75; Pages:76 to 100; Pages:101 to 117 by : Alireza Ranjbar-Motlagh
Download or read book Analysis On Metric-Measure Spaces: to 25; Pages:26 to 50; Pages:51 to 75; Pages:76 to 100; Pages:101 to 117 written by Alireza Ranjbar-Motlagh and published by . This book was released on 1998 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Measure Theory by : Terence Tao
Download or read book An Introduction to Measure Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2021-09-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Download or read book Metric Spaces written by Satish Shirali and published by Springer Science & Business Media. This book was released on 2006 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily
Book Synopsis Metric Spaces and Complex Analysis by : Amar Kumar Banerjee
Download or read book Metric Spaces and Complex Analysis written by Amar Kumar Banerjee and published by New Age International. This book was released on 2008 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lebesgue and Sobolev Spaces with Variable Exponents by : Lars Diening
Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer. This book was released on 2011-03-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Download or read book Real Analysis written by N. L. Carothers and published by Cambridge University Press. This book was released on 2000-08-15 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.
Book Synopsis Measure, Integration & Real Analysis by : Sheldon Axler
Download or read book Measure, Integration & Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/
