Abstract
Among the most significant developments in recent years in the field of generalised functions has been the appearance of the non-linear theories of Colombeau and others. The new generalised functions of Colombeau [1], [2], [3], [4], include distributions as a special sub-class, together with various non-linear functions of them. In particular the multiplication problem is comprehensively solved and expressions such as δ2, δ3 and so on are meaningful. There are, however, difficulties in presenting such theories at an elementary level, particularly to a non-specialist audience of, say, physicists and engineers to whom the material is nevertheless important and valuable. Much of the conceptual difficulty arises from the need to introduce a generalised (complex) number system whose structure is not as readily accessible to intuition as could be desired.
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Hoskins, R.F., Pinto, J.S. (1993). Nonstandard Treatments of New Generalised Functions. In: Pathak, R.S. (eds) Generalized Functions and Their Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1591-7_9
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DOI: https://doi.org/10.1007/978-1-4899-1591-7_9
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