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Proceedings of the American Mathematical Society

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A nonstandard delta function


Author: Todor Todorov
Journal: Proc. Amer. Math. Soc. 110 (1990), 1143-1144
MSC: Primary 46F10; Secondary 03H05, 26E35
MathSciNet review: 1037226
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Abstract: We prove that the Dirac delta distribution has a kernel in the class of the pointwise nonstandard functions.


References [Enhancements On Off] (What's this?)

  • [1] 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
  • [2] 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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1037226-6
Keywords: Nonstandard analysis, nonstandard extension, saturation principle, delta function
Article copyright: © Copyright 1990 American Mathematical Society