Abstract
Nonstandard Analysis suggests several ways in which the standard theories of distributions and other generalised functions could be reformulated. This paper reviews the contributions of José Sousa Pinto to this area up to his untimely death four years ago. Following the original presentation of nonstandard models for the Sebastião e Silva axiomatic treatment of distributions and ultradistributions he worked on a nonstandard theory of Sato hyperfunctions, using a simple ultrapower model of the hyperreals. (This in particular allows nonstandard representations for generalised distributions, such as those of Roumieu, Beurling, and so on.) He also considered a nonstandard theory for the generalised functions of Colombeau, and finally turned his attention to the hyperfinite representation of generalised functions, following the work of Kinoshita.
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Hoskins, R.F. (2007). The Sousa Pinto approach to nonstandard generalised functions. In: van den Berg, I., Neves, V. (eds) The Strength of Nonstandard Analysis. Springer, Vienna. https://doi.org/10.1007/978-3-211-49905-4_6
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DOI: https://doi.org/10.1007/978-3-211-49905-4_6
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