Title

Asymptotic Functions and the Problem of Multiplication of Distributions

Author Info

Todor D. Todorov, Institute of Nuclear Research and Nuclear Energy, BulgariaFollow

Recommended Citation

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.

Abstract

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].

Disciplines

Mathematics

Copyright

1981 Heron Press Limited.