Postprint version. Published in Bulgarian Journal of Physics, Volume 8, Issue 2, January 1, 1981, pages 109-120.
NOTE: At the time of publication, the author Todor D. Todorov was not yet affiliated with Cal Poly.
The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the Schwartz distributions. They are mappings of the set of the asymptotic numbers (1, 3, 5, 6) into itself. On its part, the set of the asymptotic numbers is a totally-ordered set of generalized numbers including the systems of real and complex numbers, as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the Schwartz distributions have realizations, in a certain sense, as asymptotic functions. The motivations of this work are connected with some physical problems of quantum theory [18, 25].
1981 Heron Press Limited.