Cesàro's theorems for complex sequences (Q1323108)

The classical Cesàro theorems apply to ratios of real-valued sequences like \(f_ n/g_ n\), where \hbox{\(g_ n\to\infty\)} monotonically, or \(f_ n\to 0\), and \(g_ n\to 0\) monotonically. Here such results are generalized to complex-valued sequences and, at the same time, the restriction of monotonicity on \(g_ n\) is removed in the real case. Such a condition is replaced with a more general property that does not require the ordering of the range. An application to the asymptotics of linear difference equations is presented.