Lectures on Analysis on Metric Spaces PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lectures on Analysis on Metric Spaces PDF full book. Access full book title Lectures on Analysis on Metric Spaces by Juha Heinonen. Download full books in PDF and EPUB format.
Author: Juha Heinonen
Publisher: Springer Science & Business Media
ISBN: 1461301319
Category : Mathematics
Languages : en
Pages : 149
Get Book Here
Book Description
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.
Author: Juha Heinonen
Publisher: Springer Science & Business Media
ISBN: 1461301319
Category : Mathematics
Languages : en
Pages : 149
Get Book Here
Book Description
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.
Author: Luigi Ambrosio
Publisher: Oxford University Press, USA
ISBN: 9780198529385
Category : Mathematics
Languages : en
Pages : 148
Get Book Here
Book Description
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.
Author: Fabrice Baudoin
Publisher: Springer Nature
ISBN: 3030841413
Category : Mathematics
Languages : en
Pages : 312
Get Book Here
Book Description
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.
Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 376438722X
Category : Mathematics
Languages : en
Pages : 333
Get Book Here
Book Description
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.
Author: S. Kumaresan
Publisher: Alpha Science Int'l Ltd.
ISBN: 9781842652503
Category : Computers
Languages : en
Pages : 172
Get Book Here
Book Description
"Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.
Author: Luigi Ambrosio
Publisher: Edizioni della Normale
ISBN: 9788876422553
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
This book contains the notes of an international summer school on Analysis in Metric Spaces. The contributions are the following: T. Coulhon, Random walks and geometry on infinite graphs; G. David, Uniform rectifiability and quasiminimal sets; P. Koskela, Upper gradients and Poincaré inequalities; S. Semmes, Derivatives and difference quotients for Lipschitz or Sobolev functions on various spaces; R. L. Wheeden, Some weighted Poincaré estimates in spaces of homogenous type.
Author: John R. Giles
Publisher: Cambridge University Press
ISBN: 9780521359283
Category : Mathematics
Languages : en
Pages : 276
Get Book Here
Book Description
This is an introduction to the analysis of metric and normed linear spaces for undergraduate students in mathematics. Assuming a basic knowledge of real analysis and linear algebra, the student is exposed to the axiomatic method in analysis and is shown its power in exploiting the structure of fundamental analysis, which underlies a variety of applications. An example is the link between normed linear spaces and linear algebra; finite dimensional spaces are discussed early. The treatment progresses from the concrete to the abstract: thus metric spaces are studied in some detail before general topology is begun, though topological properties of metric spaces are explored in the book. Graded exercises are provided at the end of each section; in each set the earlier exercises are designed to assist in the detection of the structural properties in concrete examples while the later ones are more conceptually sophisticated.
Author: Juha Heinonen
Publisher: Cambridge University Press
ISBN: 1107092345
Category : Mathematics
Languages : en
Pages : 447
Get Book Here
Book Description
This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
Author: Juha Heinonen
Publisher:
ISBN: 9789513923181
Category : Function spaces
Languages : fi
Pages : 77
Get Book Here
Book Description
Author: Finnur Lárusson
Publisher: Cambridge University Press
ISBN: 1139511041
Category : Mathematics
Languages : en
Pages : 128
Get Book Here
Book Description
This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The author's exposition is concise and to the point, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced students who need a foundation in real analysis.
