Abstract

The class F of "quasi-extended asymptotic functions" introduced in the present paper contains all extended asymptotic functions [8, (3.1)] (in particular, all examples constructed in [9, Sec. 1 ]). But F contains also some new asymptotic functions very similar to tht Schwartz distributions. On the other hand, every two quasi-extended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square &# 948;2 of an asymptotic function &# 948; similar to Dirac's delta-function is constructed as an example. The connection with the asymptotic functions introduced in [2] and [4] is established.

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URL: http://digitalcommons.calpoly.edu/math_fac/86