Generalized Functions and Infinitesimals

It has been widely believed for half a century t hat there will never exist a nonlinear theory of generalized functions, in any mathematica l context. The aim of this text is to show the converse is the case and invite the reader to p artici ate in the debate and to examine the consequences at an unexpectedly elementary level. T h paradox appears as another instance of the historical controversy on the existence of i nfin tesimals in mathematics, which provides a connection with nonstandard analysis. This text i s he written version of a talk at the meeting of Nonstandard Analysis, Pisa, june 2006. Math. Subject Classification. primary: 46F30, secondary: 03H99, 35D05, 35D10, 35 L67, 35R05, 82D20, 83C35, 83C57, 83C75

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