Cesàro's theorems for complex sequences
type: Item
instance of: scholarly article
title: Cesàro's theorems for complex sequences
zbMATH Open document ID: 0795.40002
author: Renato Spigler
author: Marco Vianello
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-06-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 566478
zbMATH Keywords: Cesàro theorems
zbMATH Keywords: complex-valued sequences
zbMATH Keywords: linear difference equations
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1403
OpenAlex ID: W2049224597
DOI: 10.1006/JMAA.1993.1403
description: scientific article; zbMATH DE number 566478