Full algebra of generalized functions and non-standard asymptotic analysis

Logic and Analysis 1 (3-4):205-234 (2008)
Abstract
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)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,304
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA

No citations found.

Similar books and articles
Daniel D. Merrill (2005). Augustus De Morgan's Boolean Algebra. History and Philosophy of Logic 26 (2):75-91.
Alexandra Shlapentokh (2002). Generalized Weak Presentations. Journal of Symbolic Logic 67 (2):787-819.
Analytics

Monthly downloads

Added to index

2010-08-24

Total downloads

6 ( #190,970 of 1,096,439 )

Recent downloads (6 months)

1 ( #231,754 of 1,096,439 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.