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Author: Gokulananda Das
Publisher: CRC Press
ISBN: 1000467627
Category : Mathematics
Languages : en
Pages : 182
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Book Description
Banach Limits and Applications provides all the results in the area of Banach limit, its extensions, generalizations and applications to various fields in one go (as far as possible). All the results in this field, after Banach introduced this concept in the year 1932 , are scattered till now. Sublinear functionals generating and dominating Banach Limit, unique Branch Limit (almost convergence), invariant means and invariant limits, absolute and strong almost convergence, applications to ergodicity, law of large number, Fourier series, uniform distribution of sequences, uniform density, core theorems, functional Banach limits are discussed in this book. Discovery of functional analysis such as Hahn-Banach theorem, Banach-Steinhaus Theorem helped the researchers to develop a modern, rich and unified theory of sequence spaces by enveloping classical summability theory via matrix transformation and the topics related to sequence spaces arose from the concept of Banach limit are presented in this book. The unique features of this book are as follows: It contains all the results in this area at one place which are scattered till now. The book is first of its kinds in the sense that there is no other competitive book . The contents of this monograph did not appear in any book form before. The audience of this book are the researchers in this area, the Ph.D. and advanced Masters students. The book is suitable for one or two semester course work for Ph. D. students, M.S. Students of North America and Europe, M. Phil and Masters Students of India.
Author: Gokulananda Das
Publisher: CRC Press
ISBN: 1000467627
Category : Mathematics
Languages : en
Pages : 182
Get Book Here
Book Description
Banach Limits and Applications provides all the results in the area of Banach limit, its extensions, generalizations and applications to various fields in one go (as far as possible). All the results in this field, after Banach introduced this concept in the year 1932 , are scattered till now. Sublinear functionals generating and dominating Banach Limit, unique Branch Limit (almost convergence), invariant means and invariant limits, absolute and strong almost convergence, applications to ergodicity, law of large number, Fourier series, uniform distribution of sequences, uniform density, core theorems, functional Banach limits are discussed in this book. Discovery of functional analysis such as Hahn-Banach theorem, Banach-Steinhaus Theorem helped the researchers to develop a modern, rich and unified theory of sequence spaces by enveloping classical summability theory via matrix transformation and the topics related to sequence spaces arose from the concept of Banach limit are presented in this book. The unique features of this book are as follows: It contains all the results in this area at one place which are scattered till now. The book is first of its kinds in the sense that there is no other competitive book . The contents of this monograph did not appear in any book form before. The audience of this book are the researchers in this area, the Ph.D. and advanced Masters students. The book is suitable for one or two semester course work for Ph. D. students, M.S. Students of North America and Europe, M. Phil and Masters Students of India.
Author: Gokulananda Das
Publisher: CRC Press
ISBN: 1000467570
Category : Mathematics
Languages : en
Pages : 230
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Book Description
Banach Limit and Applications provides all the results in the area of Banach Limit, its extensions, generalizations, and applications to various fields in one go (as far as possible). All the results in this field, after Banach introduced this concept in 1932, were scattered till now. Sublinear functionals generating and dominating Banach Limit, unique Banach Limit (almost convergence), invariant means and invariant limits, absolute and strong almost convergence, applications to ergodicity, law of large numbers, Fourier series, uniform distribution of sequences, uniform density, core theorems, and functional Banach limits are discussed in this book. The discovery of functional analysis, such as the Hahn-Banach Theorem and the Banach-Steinhaus Theorem, helped the researchers to develop a modern, rich, and unified theory of sequence spaces by encompassing classical summability theory via matrix transformations and the topics related to sequence spaces, which arose from the concept of Banach limits, all of which are presented in this book. The unique features of this book are as follows: All the results in this area which were scattered till now are in one place. The book is the first of its kind in the sense that there is no other competitive book. The contents of this monograph did not appear in any book form before. The audience of this book are the researchers in this area and Ph.D. and advanced master’s students. The book is suitable for one- or two-semester course work for Ph.D. students, M.S. students in North America and Europe, and M.Phil. and master’s students in India.
Author: Charles Chidume
Publisher: Springer Science & Business Media
ISBN: 1848821891
Category : Mathematics
Languages : en
Pages : 337
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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.
Author: Terry J. Morrison
Publisher: John Wiley & Sons
ISBN: 1118031245
Category : Mathematics
Languages : en
Pages : 380
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Book Description
A powerful introduction to one of the most active areas of theoretical and applied mathematics This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader's mathematical maturity and the ability to both understand and "do" mathematics. In so doing, Functional Analysis provides a strong springboard for further exploration on the wide range of topics the book presents, including: * Weak topologies and applications * Operators on Banach spaces * Bases in Banach spaces * Sequences, series, and geometry in Banach spaces Stressing the general techniques underlying the proofs, Functional Analysis also features many exercises for immediate clarification of points under discussion. This thoughtful, well-organized synthesis of the work of those mathematicians who created the discipline of functional analysis as we know it today also provides a rich source of research topics and reference material.
Author: Ravi P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 0387758186
Category : Mathematics
Languages : en
Pages : 373
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Book Description
In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis. This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields. This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.
Author: Marcel de Jeu
Publisher: Birkhäuser
ISBN: 3319278428
Category : Mathematics
Languages : en
Pages : 516
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Book Description
This book presents the proceedings of Positivity VII, held from 22-26 July 2013, in Leiden, the Netherlands. Positivity is the mathematical field concerned with ordered structures and their applications in the broadest sense of the word. A biyearly series of conferences is devoted to presenting the latest developments in this lively and growing discipline. The lectures at the conference covered a broad spectrum of topics, ranging from order-theoretic approaches to stochastic processes, positive solutions of evolution equations and positive operators on vector lattices, to order structures in the context of algebras of operators on Hilbert spaces. The contributions in the book reflect this variety and appeal to university researchers in functional analysis, operator theory, measure and integration theory and operator algebras. Positivity VII was also the Zaanen Centennial Conference to mark the 100th birth year of Adriaan Cornelis Zaanen, who held the chair of Analysis in Leiden for more than 25 years and was one of the leaders in the field during his lifetime.
Author: Manfred Einsiedler
Publisher: Springer
ISBN: 3319585401
Category : Mathematics
Languages : en
Pages : 626
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Book Description
This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory. In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.
Author:
Publisher:
ISBN:
Category : Mathematical analysis
Languages : de
Pages : 618
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Book Description
Author: Michel Ledoux
Publisher: Springer Science & Business Media
ISBN: 3642202128
Category : Mathematics
Languages : en
Pages : 493
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Book Description
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
Author: Desmond Peter Fearnley-Sander
Publisher:
ISBN:
Category : Banach spaces
Languages : en
Pages :
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Book Description
