Silverman–Toeplitz theorem

In mathematics, the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in summability theory characterizing matrix summability methods that are regular. A regular matrix summability method is a matrix transformation of a convergent sequence which preserves the limit.[1]

An infinite matrix with complex-valued entries defines a regular summability method if and only if it satisfies all of the following properties:

(every column sequence converges to 0)
(the row sums converge to 1)
(the absolute row sums are bounded).

References

  1. Silverman-Toeplitz theorem, by Ruder, Brian, Published 1966, Call number LD2668 .R4 1966 R915, Publisher Kansas State University, Internet Archive
This article is issued from Wikipedia - version of the 9/28/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.