Nonstandard Analysis : Theory and Applications

Leif O. Arkeryd

ISBN 10: 9401063354 / ISBN 13: 9789401063357

Verlag: Springer Netherlands, Springer Netherlands, 2012

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 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.

Bestandsnummer des Verkäufers 9789401063357

Bibliografische Details

• Titel: Nonstandard Analysis : Theory and Applications
• Verlag: Springer Netherlands, Springer Netherlands
• Erscheinungsjahr: 2012
• Sprache: Englisch
• ISBN-10: 9401063354
• ISBN-13: 9789401063357
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 240B x 160 H x 21 T Millimeter Breite: 240 mm, Höhe: 160 mm, Tiefe: 21 mm
• Gewicht: 612 Gramm

Über diesen Titel

Inhaltsangabe

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.

Reseña del editor

This book presents a careful and detailed introduction to the methodology of nonstandard analysis and the foundations of its use in analysis, topology, probability theory and stochastic analysis. Further articles expound recent, more advanced applications in functional analysis, stochastic differential equations, mathematical physics and mathematical finance theory. All authors are world leaders in the subject.
Audience: All mathematicians at postgraduate level and beyond who wish to learn the basics of nonstandard analysis and its role in current mathematical research.