Some Tauberian theorems for four-dimensional Euler and Borel summability

被引：0

作者：

Nuray, Fatih ^{[1
,2
]}

Patterson, Richard F. ^{[2
]}

机构：

[1] Afyon Kocatepe Univ, Dept Math, Afyon, Turkey

[2] Univ N Florida, Dept Math & Stat, Jacksonville, FL USA

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2015年

关键词：

Tauberian condition; Euler-Knopp means; Borel method; four-dimensional summability method; double sequences; Pringsheim limit;

D O I：

10.1186/s13662-015-0381-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The four-dimensional summability methods of Euler and Borel are studied as mappings from absolutely convergent double sequences into themselves. Also the following Tauberian results are proved: if x = (x(m,n)) is a double sequence that is mapped into l(2) by the four-dimensional Borel method and the double sequence x satisfies Sigma(infinity)(m-0) Sigma(infinity)(n=0)vertical bar Delta 10x(m,n)vertical bar root mn < infinity and Sigma(infinity)(m=0) Sigma(infinity)(n=0)vertical bar Delta 01x(m,n)vertical bar root mn < infinity, the x itself is in l(2).

引用

页数：8