Nonstandard Methods in Functional Analysis

This book PDF is perfect for those who love Mathematics genre, written by Siu-Ah Ng and published by World Scientific which was released on 28 May 2024 with total hardcover pages 339. You could read this book directly on your devices with pdf, epub and kindle format, check detail and related Nonstandard Methods in Functional Analysis books below.

Nonstandard Methods in Functional Analysis

Author	: Siu-Ah Ng
File Size	: 50,7 Mb
Publisher	: World Scientific
Language	: English
Release Date	: 28 May 2024
ISBN	: 9789814287555
Pages	: 339 pages

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Nonstandard Methods in Functional Analysis by Siu-Ah Ng Book PDF Summary

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.

Nonstandard Methods in Functional Analysis by Siu-Ah Ng

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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by Mauro Di Nasso,Isaac Goldbring,Martino Lupini

The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account

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Nonstandard Analysis in Practice by Francine Diener,Marc Diener

This book introduces the graduate mathematician and researcher to the effective use of nonstandard analysis (NSA). It provides a tutorial introduction to this modern theory of infinitesimals, followed by nine examples of applications, including complex analysis, stochastic differential equations, differential geometry, topology, probability, integration, and asymptotics. It ends with remarks

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Non standard Analysis by Abraham Robinson

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

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Radically Elementary Probability Theory by Edward Nelson

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.

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Nonstandard Methods in Fixed Point Theory by Asuman G. Aksoy,Mohamed A. Khamsi

A unified account of the major new developments inspired by Maurey's application of Banach space ultraproducts to the fixed point theory for non-expansive mappings is given in this text. The first third of the book is devoted to laying a careful foundation for the actual fixed point theoretic results which

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Nonstandard Methods in Stochastic Analysis and Mathematical Physics by Sergio Albeverio,Jens Erik Fenstad,Raphael Høegh-Krohn,Tom Lindstrøm

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.

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Nonstandard Analysis for the Working Mathematician by Peter A. Loeb,Manfred P. H. Wolff

Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a ‘secret weapon’ by those

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