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Advances in Analysis, Probability and Mathematical Physics

Contributions of Nonstandard Analysis

  • Book
  • © 1995

Overview

Editors:
  1. Sergio A. Albeverio

    1. Faculty of Mathematics, Ruhr-Universität Bochum, Bochum, Germany

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  2. Wilhelm A. J. Luxemburg

    1. Department of Mathematics, California Institute of Technology, Pasadena, USA

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  3. Manfred P. H. Wolff

    1. Mathematical Institute, University of Tübingen, Tübingen, Germany

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Part of the book series: Mathematics and Its Applications (MAIA, volume 314)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-x
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  2. Analysis

    1. Front Matter

      Pages 1-1
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    2. Singular Traces and Nonstandard Analysis

      • S. Albeverio, D. Guido, A. Ponosov, S. Scarlatti
      Pages 3-19

    3. Navier-Stokes Equations

      • M. Capiński, N. J. Cutland
      Pages 20-36

    4. Hyperfinite Approximations of Commutative Topological Groups

      • E. I. Gordon
      Pages 37-45

    5. A Note on the Myope Topology

      • Tommy Norberg
      Pages 46-55

    6. Nonlinear Theories of Generalized Functions

      • Michael Oberguggenberger
      Pages 56-74

    7. A Nonstandard Approach to the Pettis Integral

      • Horst Osswald
      Pages 75-90

    8. A Counterexample to the Spectral Mapping Theorem Revisited from a Nonstandard Point of View

      • H. Ploss
      Pages 91-95

    9. Nonstandard polynomials in several variables

      • Hermann Render
      Pages 96-106

    10. An Existence Result for a Class of Partial Differential Equations with Smooth Coefficients

      • Todor Todorov
      Pages 107-121

    11. On the Generation of Topology by External Equivalence-Relations

      • Bernd Wietschorke
      Pages 122-131

    12. Nonstandard hulls of Lebesgue-Bochner spaces

      • G. Beate Zimmer
      Pages 132-139
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Keywords

About this book

In 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he called `Nonstandard analysis'. `Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of numbers was closely related to the ring of Schmieden and Laugwitz, developed independently a few years earlier.
During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research.
Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics.
This volume can be used as a complementary text to courses in nonstandard analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics.

Editors and Affiliations

  • Faculty of Mathematics, Ruhr-Universität Bochum, Bochum, Germany

    Sergio A. Albeverio

  • Department of Mathematics, California Institute of Technology, Pasadena, USA

    Wilhelm A. J. Luxemburg

  • Mathematical Institute, University of Tübingen, Tübingen, Germany

    Manfred P. H. Wolff

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