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Pointwise kernels of Schwartz distributions


Author: Todor Todorov
Journal: Proc. Amer. Math. Soc. 114 (1992), 817-819
MSC: Primary 46F05; Secondary 03H05, 30G06, 46S20
DOI: https://doi.org/10.1090/S0002-9939-1992-1081703-0
MathSciNet review: 1081703
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Abstract: We show that Schwartz distributions have kernels in the class of the pointwise nonstandard functions.


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

  • [1] J. F. Colombeau, New generalized functions and multiplication of distributions, North-Holland Math. Stud., vol. 84, North-Holland, Amsterdam and New York, 1984. MR 738781 (86c:46042)
  • [2] L. Schwartz, Theorie des distributions I, II, Herman, Paris, 1950, 1951. MR 0209834 (35:730)
  • [3] K. D. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals, Academic Press, New York, 1976. MR 0491163 (58:10429)
  • [4] T. Todorov, A nonstandard delta function, Proc. Amer. Math. Soc. 110 (1990), 1143-1144. MR 1037226 (91c:46060)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1081703-0
Keywords: Nonstandard extension, transfer principle, Schwartz distribution, kernel, multiplication of distributions
Article copyright: © Copyright 1992 American Mathematical Society

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