Matrix characterization of oscillation for double sequences |
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| Authors: | Richard F. Patterson Jeff Connor Jeannette Kline |
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| Affiliation: | (1) Department of Mathematics and Statistics, University of North Florida, building 14, Jacksonville, Florida 32224, USA;(2) Mathematics Department, Ohio University, Athens, Ohio 45701, USA;(3) Department of Mathematics, Washington and Jefferson College, 60 S. Lincoln St., Washington, PA 15301, USA |
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| Abstract: | 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. |
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| Keywords: | double sequence p-convergent oscillation, double oscillations |
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