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Author : Juha Heinonen
Publisher :
ISBN 13 : 9789513923181
Total Pages : 77 pages
Book Rating : 4.9/5 (231 download)
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:
Author : Juha Heinonen
Publisher : Springer Science & Business Media
ISBN 13 : 9780387951041
Total Pages : 158 pages
Book Rating : 4.9/5 (51 download)
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 2001 with total page 158 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.
Author : Asen L. Dontchev
Publisher : Springer Nature
ISBN 13 : 3030799115
Total Pages : 223 pages
Book Rating : 4.0/5 (37 download)
Download or read book Lectures on Variational Analysis written by Asen L. Dontchev and published by Springer Nature. This book was released on 2022-02-04 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.
Author : J. Yeh
Publisher : World Scientific
ISBN 13 : 9789810239411
Total Pages : 568 pages
Book Rating : 4.2/5 (394 download)
Download or read book Lectures on Real Analysis written by J. Yeh and published by World Scientific. This book was released on 2000 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the Lebesgue integral is a main pillar in the foundation of modern analysis and its applications, including probability theory. This volume shows how and why the Lebesgue integral is such a universal and powerful concept. The lines of development of the theory are made clear by the order in which the main theorems are presented. Frequent references to earlier theorems made in the proofs emphasize the interdependence of the theorems and help to show how the various definitions and theorems fit together. Counter-examples are included to show why a hypothesis in a theorem cannot be dropped. The book is based upon a course on real analysis which the author has taught. It is particularly suitable for a one-year course at the graduate level. Precise statements and complete proofs are given for every theorem, with no obscurity left. For this reason the book is also suitable for self-study.
Author : Ştefan Cobzaş
Publisher : Springer
ISBN 13 : 3030164896
Total Pages : 605 pages
Book Rating : 4.0/5 (31 download)
Download or read book Lipschitz Functions written by Ştefan Cobzaş and published by Springer. This book was released on 2019-05-23 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.
Author : Juha Heinonen
Publisher : Springer Science & Business Media
ISBN 13 : 1461301319
Total Pages : 149 pages
Book Rating : 4.4/5 (613 download)
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.
Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 9780691084190
Total Pages : 444 pages
Book Rating : 4.0/5 (841 download)
Download or read book Beijing Lectures in Harmonic Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 1986-11-21 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on seven lecture series given by leading experts at a summer school at Peking University, in Beijing, in 1984. this book surveys recent developments in the areas of harmonic analysis most closely related to the theory of singular integrals, real-variable methods, and applications to several complex variables and partial differential equations. The different lecture series are closely interrelated; each contains a substantial amount of background material, as well as new results not previously published. The contributors to the volume are R. R. Coifman and Yves Meyer, Robert Fcfferman, Carlos K. Kenig, Steven G. Krantz, Alexander Nagel, E. M. Stein, and Stephen Wainger.
Author : Walter Neumann
Publisher : Springer Nature
ISBN 13 : 3030618072
Total Pages : 356 pages
Book Rating : 4.0/5 (36 download)
Download or read book Introduction to Lipschitz Geometry of Singularities written by Walter Neumann and published by Springer Nature. This book was released on 2021-01-11 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.
Author : José M. Amigó
Publisher : Springer Nature
ISBN 13 : 3031300149
Total Pages : 273 pages
Book Rating : 4.0/5 (313 download)
Download or read book Functional Analysis and Continuous Optimization written by José M. Amigó and published by Springer Nature. This book was released on 2023-07-01 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16–17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.
Author : Gerald Beer
Publisher : CRC Press
ISBN 13 : 1000884309
Total Pages : 243 pages
Book Rating : 4.0/5 (8 download)
Download or read book Bornologies and Lipschitz Analysis written by Gerald Beer and published by CRC Press. This book was released on 2023-05-15 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of its members. The largest bornology is the power set of the space and the smallest is the bornology of its finite subsets. Between these lie (among others) the metrically bounded subsets, the relatively compact subsets, the totally bounded subsets, and the Bourbaki bounded subsets. Classes of functions are intimately connected to various bornologies; e.g., (1) a function is locally Lipschitz if and only if its restriction to each relatively compact subset is Lipschitz; (2) a subset is Bourbaki bounded if and only if each uniformly continuous function on the space is bounded when restricted to the subset. A great deal of attention is given to the variational notions of strong uniform continuity and strong uniform convergence with respect to the members of a bornology, leading to the bornology of UC-subsets and UC-spaces. Spaces on which its uniformly continuous real-valued functions are stable under pointwise product are characterized in terms of the coincidence of the Bourbaki bounded subsets with a usually larger bornology. Special attention is given to Lipschitz and locally Lipschitz functions. For example, uniformly dense subclasses of locally Lipschitz functions within the real-valued continuous functions, Cauchy continuous functions, and uniformly continuous functions are presented. It is shown very generally that a function between metric spaces has a particular metric property if and only if whenever it is followed in a composition by a real-valued Lipschitz function, the composition has the property. Bornological convergence of nets of closed subsets, having Attouch-Wets convergence as a prototype, is considered in detail. Topologies of uniform convergence for continuous linear operators between normed spaces is explained in terms of the bornological convergence of their graphs. Finally, the idea of a bornological extension of a topological space is presented, and all regular extensions can be so realized.
Author : Nik Weaver
Publisher : World Scientific
ISBN 13 : 9789810238735
Total Pages : 242 pages
Book Rating : 4.2/5 (387 download)
Download or read book Lipschitz Algebras written by Nik Weaver and published by World Scientific. This book was released on 1999 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C(omega) and Linfinity(X), for omega a compact Hausdorff space and X a sigma-finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.
Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 1400882095
Total Pages : 435 pages
Book Rating : 4.4/5 (8 download)
Download or read book Beijing Lectures in Harmonic Analysis. (AM-112), Volume 112 written by Elias M. Stein and published by Princeton University Press. This book was released on 2016-03-02 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on seven lecture series given by leading experts at a summer school at Peking University, in Beijing, in 1984. this book surveys recent developments in the areas of harmonic analysis most closely related to the theory of singular integrals, real-variable methods, and applications to several complex variables and partial differential equations. The different lecture series are closely interrelated; each contains a substantial amount of background material, as well as new results not previously published. The contributors to the volume are R. R. Coifman and Yves Meyer, Robert Fcfferman, Carlos K. Kenig, Steven G. Krantz, Alexander Nagel, E. M. Stein, and Stephen Wainger.
Author : R. Tyrrell Rockafellar
Publisher : Springer Science & Business Media
ISBN 13 : 3642024319
Total Pages : 747 pages
Book Rating : 4.6/5 (42 download)
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Author : Mikhail S. Agranovich
Publisher : Springer
ISBN 13 : 3319146483
Total Pages : 343 pages
Book Rating : 4.3/5 (191 download)
Download or read book Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains written by Mikhail S. Agranovich and published by Springer. This book was released on 2015-05-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.
Author : Alexandre Ern
Publisher : Springer Nature
ISBN 13 : 3030563413
Total Pages : 325 pages
Book Rating : 4.0/5 (35 download)
Download or read book Finite Elements I written by Alexandre Ern and published by Springer Nature. This book was released on 2021-03-22 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.
Author : Lionel Thibault
Publisher : World Scientific
ISBN 13 : 981125818X
Total Pages : 1629 pages
Book Rating : 4.8/5 (112 download)
Download or read book Unilateral Variational Analysis In Banach Spaces (In 2 Parts) written by Lionel Thibault and published by World Scientific. This book was released on 2023-02-14 with total page 1629 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph provides a detailed and comprehensive presentation of the rich and beautiful theory of unilateral variational analysis in infinite dimensions. It is divided into two volumes named Part I and Part II. Starting with the convergence of sets and the semilimits and semicontinuities of multimappings, the first volume develops the theories of tangent cones, of subdifferentials, of convexity and duality in locally convex spaces, of extended mean value inequalities in absence of differentiability, of metric regularity, of constrained optimization problems.The second volume is devoted to special classes of non-smooth functions and sets. It expands the theory of subsmooth functions and sets, of semiconvex functions and multimappings, of primal lower regular functions, of singularities of non-smooth mappings, of prox-regular functions and sets in general spaces, of differentiability of projection mapping and others for prox-regular sets. Both volumes I and II contain, for each chapter, extensive comments covering related developments and historical comments.Connected area fields of the material are: optimization, optimal control, variational inequalities, differential inclusions, mechanics, economics. The book is intended for PhD students, researchers, and practitioners using unilateral variational analysis tools.
Author : Cornelia Druţu
Publisher : American Mathematical Soc.
ISBN 13 : 1470411040
Total Pages : 841 pages
Book Rating : 4.4/5 (74 download)
Download or read book Geometric Group Theory written by Cornelia Druţu and published by American Mathematical Soc.. This book was released on 2018-03-28 with total page 841 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.
