Lectures on Analysis on Metric Spaces
Lectures on Analysis on Metric Spaces

Author: Juha Heinonen

Publisher: Springer Science & Business Media

Published: 2001

Total Pages: 158

ISBN-13: 9780387951041

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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.

Introduction to Lipschitz Geometry of Singularities
Introduction to Lipschitz Geometry of Singularities

Author: Walter Neumann

Publisher: Springer Nature

Published: 2021-01-11

Total Pages: 356

ISBN-13: 3030618072

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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all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves.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.

Lectures on Variational Analysis
Lectures on Variational Analysis

Author: Asen L. Dontchev

Publisher: Springer Nature

Published: 2022-02-04

Total Pages: 223

ISBN-13: 3030799115

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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.

Lipschitz Functions
Lipschitz Functions

Author: Ştefan Cobzaş

Publisher: Springer

Published: 2019-05-23

Total Pages: 605

ISBN-13: 3030164896

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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.

Functional Analysis and Continuous Optimization
Functional Analysis and Continuous Optimization

Author: José M. Amigó

Publisher: Springer Nature

Published: 2023-07-01

Total Pages: 273

ISBN-13: 3031300149

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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.

Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University
Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

Author: Maxim Olegovich Korpusov

Publisher: World Scientific

Published: 2021-12-28

Total Pages: 377

ISBN-13: 981124894X

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This book is a systematic presentation of basic notions, facts, and ideas of nonlinear functional analysis and their applications to nonlinear partial differential equations. It begins from a brief introduction to linear functional analysis, including various types of convergence and functional spaces. The main part of the book is devoted to the theory of nonlinear operators. Various methods of the study of nonlinear differential equations based on the facts of nonlinear analysis are presented in detail. This book may serve as an introductory textbook for students and undergraduates specializing in modern mathematical physics.

Lectures on Clifford (Geometric) Algebras and Applications
Lectures on Clifford (Geometric) Algebras and Applications

Author: Rafal Ablamowicz

Publisher: Springer Science & Business Media

Published: 2011-06-28

Total Pages: 231

ISBN-13: 0817681906

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The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.

Mathematical Analysis, Probability and Applications – Plenary Lectures
Mathematical Analysis, Probability and Applications – Plenary Lectures

Author: Tao Qian

Publisher: Springer

Published: 2016-08-25

Total Pages: 335

ISBN-13: 3319419455

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This book collects lectures given by the plenary speakers at the 10th International ISAAC Congress, held in Macau, China in 2015. The contributions, authored by eminent specialists, present some of the most exciting recent developments in mathematical analysis, probability theory, and related applications. Topics include: partial differential equations in mathematical physics, Fourier analysis, probability and Brownian motion, numerical analysis, and reproducing kernels. The volume also presents a lecture on the visual exploration of complex functions using the domain coloring technique. Thanks to the accessible style used, readers only need a basic command of calculus.

Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains
Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains

Author: Mikhail S. Agranovich

Publisher: Springer

Published: 2015-05-06

Total Pages: 343

ISBN-13: 3319146483

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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.