Mercerian theorems involving Cesàro means of positive order

A. Jakimovski, D. C. Russell

Research output: Contribution to journalArticlepeer-review

Abstract

If Cα denotes the Cesàro matrix of arbitrary positive order α, we investigate the set Dα of complex numbers μ for which the sequence-to-sequence transformation defined by the matrix I-μCα is equivalent to convergence. In particular, we show that Dα is strictly decreasing as α increases. Most previous investigations have taken μ real and/or α an integer; we make no such restrictions.

Original languageEnglish
Pages (from-to)119-131
Number of pages13
JournalMonatshefte fur Mathematik
Volume96
Issue number2
DOIs
StatePublished - Jun 1983

Fingerprint

Dive into the research topics of 'Mercerian theorems involving Cesàro means of positive order'. Together they form a unique fingerprint.

Cite this