| Abstract: |
| Let $({\mathcal U},\hslash)$ be a pair
consisting of a module $\mathcal U$ over the ring of proper rational functions and a nonzero
element $\hslash\in {\mathcal U}$. Elements of ${\mathcal U}$ are interpreted as classical functions, with $\hslash$
representing the constant function 1; multiplication by the local parameter is viewed as the integration operator. We
assume that the zero function is the only constant function that arises as an integral.
Within this framework, we introduce Schwartz distributions of finite order and study linear dynamic equations,
encompassing linear differential and difference equations, as well as more general linear dynamic equations on time scales.
Acknowledgment: This work was supported by Shota Rustaveli National Science Foundation
of Georgia (SRNSFG) [FR-24-8249]. |
|