Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2018-03-29
An Easy Approach to Distributions and Operational CalculusVakhtang Lomadze (1) Javakhishvili Tbilisi State University, Tbilisi, Georgia
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 defined 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.
Keywords: Mikusinski functions, distributions, operational calculus
Lomadze Vakhtang: An Easy Approach to Distributions and Operational Calculus. Z. Anal. Anwend. 37 (2018), 151-158. doi: 10.4171/ZAA/1607