Mercerian theorems involving Cesàro means of positive order

A. Jakimovski; D. C. Russell

doi:10.1007/BF01530688

Mercerian theorems involving Cesàro means of positive order

A. Jakimovski, D. C. Russell

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	119-131
Number of pages	13
Journal	Monatshefte fur Mathematik
Volume	96
Issue number	2
DOIs	https://doi.org/10.1007/BF01530688
State	Published - Jun 1983

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abstract = "If Cα denotes the Ces{\`a}ro 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.",

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Mercerian theorems involving Cesàro means of positive order

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