Logic and Analysis 1 (3-4):205-234 (2008)

We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a connection between our theory with non-standard analysis and thus answer, although indirectly, a question raised by Colombeau. This article provides a bridge between Colombeau theory of generalized functions and non-standard analysis
Keywords Schwartz distributions  Generalized functions  Colombeau algebra  Multiplication of distributions  Non-standard analysis  Infinitesimals  Ultrapower non-standard model  Ultrafilter  Maximal filter  Robinson valuation field  Ultra-metric  Hahn–Banach theorem
Categories (categorize this paper)
DOI 10.1007/s11813-008-0008-y
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,265
Through your library

References found in this work BETA

Applied Nonstandard Analysis.Martin Davis - 1978 - Journal of Symbolic Logic 43 (2):383-384.
General Topology.John L. Kelley - 1962 - Journal of Symbolic Logic 27 (2):235-235.
Nonarchimedean Fields and Asymptotic Expansions.A. H. Lightstone & Abraham Robinson - 1981 - Journal of Symbolic Logic 46 (1):163-164.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles


Added to PP index

Total views
55 ( #206,687 of 2,507,715 )

Recent downloads (6 months)
3 ( #209,449 of 2,507,715 )

How can I increase my downloads?


My notes