Nonstandard principles for generalized functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:384

Article

Vernaeve, H.

关键词: Nonlinear generalized functions;    Nonstandard analysis;    Ultrafilter;    Filter;   

DOI  :  10.1016/j.jmaa.2011.06.002

来源: Elsevier

【 摘 要 】

We show that principles from nonstandard analysis hold to some extent for nonlinear generalized functions. The generalized functions under consideration are constructed as families of functions modulo a free filter, as it is usually done in applied analysis. In contrast with models of nonstandard analysis, we do not require the filter to be an ultrafilter. The principles are intended to be used as a tool for proving theorems, which we illustrate by means of an automatic continuity result that was not suspected by experts in the field. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free