One more (a further) generalization of the Final Value Theorem

Abstract

It is shown that the previous [1-3] generalization of the final-value theorem to the average (not necessarily limiting) values, can be extended to the higher-order running averages $(<{>}_t),li{m}_{s\to 0}[sF(s)]=li{m}_{t\to \infty }<<...<<f({\lambda }_q)>{\lambda }_{q-1}>{\lambda }_{q-2}...>{\lambda }_1>t$, if f(t) is such that $\exists m=min[q]<\infty$ for which the later limit exists.

Logically, this is an essential step after Ms. arXiv:1109.3356v2 [math-ph], but, by itslf, the Ms. does not present any worked-out applications, and at the present stage we just wish to keep the obtained results. 11 pages, no figures

References in corpus (1)

• On the recovery of the time average of continuous and discrete time functions from their Laplace and z-transforms

Cited by in corpus (1)

• On the recovery of the time average of continuous and discrete time functions from their Laplace and z-transforms