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- Title
Four dimensional matrix that induces the double Gibbs phenomenon.
- Authors
Patterson, R. F.; Rhoades, B. E.
- Abstract
In 1930 Knopp presented the following matrix characterization for the core of ordinary sequences. If A is a nonnegative regular matrix then the core of [ Ax] is contained in the core of [ x], provided that [ Ax] exists. Patterson in 1999 extended Knopp's results to double sequences via four dimensional matrices. In a manner similar to the Knopp's and Patterson's results we present multidimensional extensions of Bustoz's singular dimensional Gibbs phenomenon results. These results include a notion of what it means for a four dimensional matrix transformation to induce the double Gibbs phenomenon in s. In addition, necessary and sufficient conditions for a four dimensional matrix to induce the double Gibbs phenomenon is also presented.
- Subjects
GIBBS phenomenon; STOCHASTIC convergence; MATRICES (Mathematics); ABSTRACT algebra; UNIVERSAL algebra
- Publication
Acta Mathematica Hungarica, 2010, Vol 129, Issue 1/2, p142
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-010-9256-x