Author: Raymond W. FreesePublisher: Nova Publishers
ISBN: 9781590330197
Category : Mathematics
Languages : en
Pages : 314
Book Description
Geometry of Linear 2-normed Spaces
Author: Raymond W. FreesePublisher: Nova Publishers
ISBN: 9781590330197
Category : Mathematics
Languages : en
Pages : 314
Book Description
Introduction to Banach Spaces and their Geometry
Author: Publisher: Elsevier
ISBN: 0080871798
Category : Mathematics
Languages : en
Pages : 321
Book Description
Introduction to Banach Spaces and their Geometry
Normed Linear Spaces
Author: Mahlon M. DayPublisher: Springer Science & Business Media
ISBN: 3662090007
Category : Mathematics
Languages : en
Pages : 222
Book Description
Handbook of the Geometry of Banach Spaces
Author: Publisher: Elsevier
ISBN: 0080532802
Category : Mathematics
Languages : en
Pages : 1017
Book Description
The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.
Artificial Intelligence and Applied Mathematics in Engineering Problems
Author: D. Jude HemanthPublisher: Springer Nature
ISBN: 3030361780
Category : Technology & Engineering
Languages : en
Pages : 1105
Book Description
This book features research presented at the 1st International Conference on Artificial Intelligence and Applied Mathematics in Engineering, held on 20–22 April 2019 at Antalya, Manavgat (Turkey). In today’s world, various engineering areas are essential components of technological innovations and effective real-world solutions for a better future. In this context, the book focuses on problems in engineering and discusses research using artificial intelligence and applied mathematics. Intended for scientists, experts, M.Sc. and Ph.D. students, postdocs and anyone interested in the subjects covered, the book can also be used as a reference resource for courses related to artificial intelligence and applied mathematics.
Banach Space Theory
Author: Marián FabianPublisher: Springer Science & Business Media
ISBN: 1441975152
Category : Mathematics
Languages : en
Pages : 820
Book Description
Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Geometric Properties of Banach Spaces and Nonlinear Iterations
Author: Charles ChidumePublisher: Springer Science & Business Media
ISBN: 1848821891
Category : Mathematics
Languages : en
Pages : 337
Book Description
The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.
An Introduction to Banach Space Theory
Author: Robert E. MegginsonPublisher: Springer Science & Business Media
ISBN: 1461206030
Category : Mathematics
Languages : en
Pages : 613
Book Description
Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.
The Volume of Convex Bodies and Banach Space Geometry
Author: Gilles PisierPublisher: Cambridge University Press
ISBN: 9780521666350
Category : Mathematics
Languages : en
Pages : 270
Book Description
A self-contained presentation of results relating the volume of convex bodies and Banach space geometry.
Introduction to the Analysis of Normed Linear Spaces
Author: J. R. GilesPublisher: Cambridge University Press
ISBN: 9780521653756
Category : Mathematics
Languages : en
Pages : 298
Book Description
This is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. The reader need only be familiarity with elementary real and complex analysis, linear algebra and have studied a course in the analysis of metric spaces; knowledge of integration theory or general topology is not required. The text concerns the structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. The implications of the general theory are illustrated with a great variety of example spaces.