Generalized Functions and Infinitesimals

Details Generalized Functions and Infinitesimals Generalized Functions and Infinitesimals

2006-10-08

arxiv.org/abs/math/0610264v1

Mathematics

Functional Analysis

7 pages,research-expository paper

Scientific paper

It has been widely believed for half a century that there will never exist a nonlinear theory of generalized functions, in any mathematical context. The aim of this text is to show the converse is the case and invite the reader to participate in the debate and to examine the consequences at an unexpectedly elementary level. The paradox appears as another instance of the historical controversy on the existence of infinitesimals in mathematics, which provides a connection with nonstandard analysis. This text is the written version of a talk at the meeting of Nonstandard Analysis, Pisa, june 2006.

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