Quasi-asymptotic behavior at infinity of tempered operators (Q2786763)

Applications of the asymptotic behavior of ordinary functions and generalized functions in different areas such as integral transforms, quantum physics, and differential equations are known and can be gathered from easily available references. Similarly, the quasi-asymptotic behavior of Schwartz distributions was studied by many mathematicians, e.g., by \textit{V. S. Vladimirov} et al. [Tauberian theorems for generalized functions. Dordrecht (Netherlands) etc.: Kluwer Academic Publishers (1988; Zbl 0636.40003)] and \textit{S. Pilipović} et al. [Asymptotic behavior of generalized functions. Hackensack, NJ: World Scientific (2012; Zbl 1259.46001)]. The present paper initiates the study of the notion of quasi-asymptotic behavior at infinity on a subspace that is called tempered operators, which is done in Section~3. Section~4 investigates, as an application, a final value theorem for the Stieltjes transform, and in Section~5 it is established that the space of tempered operators (defined in Section~3) with sequential convergence is isomorphic to the space of tempered distributions supported on \([0,\infty)\) with tempered convergence.