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In the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and extension of Leibniz'' infinitesimal calculus. Since then, the methodology has found applications in a wide spectrum of areas in mathematics, with particular success in the probability theory and functional analysis. In the latter, fruitful results were produced with Luxemburg''s invention of the nonstandard hull construction. However, there is still no publication of a coherent and self-contained treatment of functional analysis using methods from nonstandard analysis. This publication aims to fill this gap.
Book Synopsis Nonstandard Methods in Functional Analysis by : Siu-Ah Ng
Download or read book Nonstandard Methods in Functional Analysis written by Siu-Ah Ng and published by World Scientific. This book was released on 2010 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and extension of Leibniz'' infinitesimal calculus. Since then, the methodology has found applications in a wide spectrum of areas in mathematics, with particular success in the probability theory and functional analysis. In the latter, fruitful results were produced with Luxemburg''s invention of the nonstandard hull construction. However, there is still no publication of a coherent and self-contained treatment of functional analysis using methods from nonstandard analysis. This publication aims to fill this gap.
Book Synopsis Nonstandard Methods in Functional Analysis by :
Download or read book Nonstandard Methods in Functional Analysis written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.
Book Synopsis Nonstandard Methods in Stochastic Analysis and Mathematical Physics by : Sergio Albeverio
Download or read book Nonstandard Methods in Stochastic Analysis and Mathematical Physics written by Sergio Albeverio and published by Courier Dover Publications. This book was released on 2009-02-26 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.
1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.
Book Synopsis Nonstandard Analysis by : Leif O. Arkeryd
Download or read book Nonstandard Analysis written by Leif O. Arkeryd and published by Springer Science & Business Media. This book was released on 1997-04-30 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.
This book introduces Robinson's nonstandard analysis, an application of model theory in analysis. Unlike some texts, it does not attempt to teach elementary calculus on the basis of nonstandard analysis, but points to some applications in more advanced analysis. The contents proceed from a discussion of the preliminaries to Nonstandard Models; Nonstandard Real Analysis; Enlargements and Saturated Models; Functionals, Generalized Limits, and Additive Measures; and finally Nonstandard Topology and Functional Analysis. No background in model theory is required, although some familiarity with analysis, topology, or functional analysis is useful. This self-contained book can be understood after a basic calculus course.
Book Synopsis Nonstandard Analysis by : Martin Väth
Download or read book Nonstandard Analysis written by Martin Väth and published by Springer Science & Business Media. This book was released on 2007 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces Robinson's nonstandard analysis, an application of model theory in analysis. Unlike some texts, it does not attempt to teach elementary calculus on the basis of nonstandard analysis, but points to some applications in more advanced analysis. The contents proceed from a discussion of the preliminaries to Nonstandard Models; Nonstandard Real Analysis; Enlargements and Saturated Models; Functionals, Generalized Limits, and Additive Measures; and finally Nonstandard Topology and Functional Analysis. No background in model theory is required, although some familiarity with analysis, topology, or functional analysis is useful. This self-contained book can be understood after a basic calculus course.
This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.
Book Synopsis Nonstandard Analysis and Its Applications by : Nigel Cutland
Download or read book Nonstandard Analysis and Its Applications written by Nigel Cutland and published by CUP Archive. This book was released on 1988-10-13 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.
Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
Book Synopsis Radically Elementary Probability Theory by : Edward Nelson
Download or read book Radically Elementary Probability Theory written by Edward Nelson and published by Princeton University Press. This book was released on 1987 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
Book Synopsis Non-standard Analysis by : Abraham Robinson
Download or read book Non-standard Analysis written by Abraham Robinson and published by Princeton University Press. This book was released on 2016-08-11 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.
Book Synopsis Nonstandard Analysis and Its Applications by : Nigel Cutland
Download or read book Nonstandard Analysis and Its Applications written by Nigel Cutland and published by Cambridge University Press. This book was released on 1988-09-30 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject.
Based on a conference on the interaction between functional analysis, harmonic analysis and probability theory, this work offers discussions of each distinct field, and integrates points common to each. It examines developments in Fourier analysis, interpolation theory, Banach space theory, probability, probability in Banach spaces, and more.
Book Synopsis Interaction Between Functional Analysis, Harmonic Analysis, and Probability by : Nigel Kalton
Download or read book Interaction Between Functional Analysis, Harmonic Analysis, and Probability written by Nigel Kalton and published by CRC Press. This book was released on 1995-10-12 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a conference on the interaction between functional analysis, harmonic analysis and probability theory, this work offers discussions of each distinct field, and integrates points common to each. It examines developments in Fourier analysis, interpolation theory, Banach space theory, probability, probability in Banach spaces, and more.
