The notion of oscillation for ordinary sequences was presented by Hurwitz in 1930. Using this notion Agnew and Hurwitz presented regular matrix characterization of the resulting sequence space. The primary goal of this article is to extend this definition to double sequences, which grants us the following definition: the double oscillation of a double sequence of real or complex number is given P-lim sup(m,n)→∞;(α,β)→∞|S m,n-S α,β|. Using this concept a matrix characterization of double oscillation sequence space is presented. Other implication and variation shall also be presented.
@article{bwmeta1.element.doi-10_2478_s11533-008-0034-8,
author = {Richard Patterson and Jeff Connor and Jeannette Kline},
title = {Matrix characterization of oscillation for double sequences},
journal = {Open Mathematics},
volume = {6},
year = {2008},
pages = {488-496},
zbl = {1158.40002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0034-8}
}
Richard Patterson; Jeff Connor; Jeannette Kline. Matrix characterization of oscillation for double sequences. Open Mathematics, Tome 6 (2008) pp. 488-496. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0034-8/
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