An Easy Approach to Distributions and Operational Calculus

  • Vakhtang Lomadze

    Javakhishvili Tbilisi State University, Tbilisi, Georgia

Abstract

The Mikusinski space is introduced as the smallest extension of the space of classical continuous functions in which the integration operator is bijective. (This can be viewed as a very small part of the field of Mikusinski operators.) It is shown that the space of Schwartz distributions (of finite order) can be de fined as a quotient of the Mikusinski space. A remarkable property of Mikusinski functions is that they admit multiplication by all rational functions. It is demonstrated that this multiplication provides a natural simple basis for Heaviside's operational calculus.

Cite this article

Vakhtang Lomadze, An Easy Approach to Distributions and Operational Calculus. Z. Anal. Anwend. 37 (2018), no. 2, pp. 151–158

DOI 10.4171/ZAA/1607