Advances in Analysis, Probability and Mathematical Physics Contributions of Nonstandard Analysis

Advances in Analysis, Probability and Mathematical Physics Contributions of Nonstandard Analysis / edited by Sergio Albeverio, Wilhelm A.J. Luxemburg, Manfred P.H. Wolff.

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...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Albeverio, Sergio (Editor), Luxemburg, Wilhelm A.J (Editor), Wolff, Manfred P.H (Editor)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 1995.
Edition:1st ed. 1995.
Series:Mathematics and Its Applications ; 314
Springer eBook Collection.
Subjects:
Mathematical analysis.
Analysis (Mathematics).
Statistics .
Mathematical physics.
Geometry.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Table of Content
  • I: Analysis
  • Singular traces and nonstandard analysis
  • Navier-Stokes equations
  • Hyperfinite approximations of commutative topological groups
  • A note on the myope topology
  • Nonlinear theories of generalized functions
  • A nonstandard approach to the Pettis integral
  • A counterexample to the spectral mapping theorem revisited from a nonstandard point of view
  • Nonstandard polynominals in several variables
  • An existence result for a class of partial differential equations with smooth coefficients
  • On the generation of topology by external equivalence relations
  • Nonstandard hulls of Lebesgue-Bochner spaces
  • II: Probability Theory
  • A nonstandard approach to diffusions on manifolds and nonstandard heat kernels
  • A nonstandard approach to the Malliavin Calculus
  • Ergodic transformations in AST
  • Nonstandard characterization for a general invariance principle
  • Andersons’s Brownian motion and the infinite dimensional Ornstein-Uhlenbeck process
  • Two applications of NSA in the theory of stochastic dynamical systems
  • Nonstandard methods and the space of experiments
  • III: Mathematical Physics
  • Infinite range forces and strong L1-asymptotics for the space-homogeneous Boltzmann equation
  • A nonstandard analysis approach to the theory of quantum meanfield systems.

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