A nonstandard delta function
Abstract: We prove that the Dirac delta distribution has a kernel in the class of the pointwise nonstandard functions.
-  Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
-  K. D. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, No. 72. MR 0491163
Keywords: Nonstandard analysis, nonstandard extension, saturation principle, delta function
Article copyright: © Copyright 1990 American Mathematical Society