Some Tauberian theorems for four-dimensional Euler and Borel summability
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 = (xm,n) is a double sequence that is mapped into ℓ2 by the four-dimensional Borel method and the double sequence x satisfies (Formula presented.) and (Formula presented.), then x itself is in ℓ2.
Advances in Difference Equations
Digital Object Identifier (DOI)
Nuray, & Patterson, R. F. (2015). Some Tauberian theorems for four-dimensional Euler and Borel summability. Advances in Difference Equations, 2015(1), 1–8. https://doi.org/10.1186/s13662-015-0381-2