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Mathematical Communications, Vol. 14 No. 1, 2009.

Original scientific paper

Four-dimensional matrix transformation and the double Gibbs' phenomenon

Richard F. Patterson ; Department of Mathematics and Statistics,University of North Florida, Jacksonville, Florida, U.S.A.
Billy E. Rhoades ; Department of Mathematics, Indiana University, Bloomington, Indiana, U.S.A.

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Abstract

In 1976 Fridy presented a series of theorems that chacterize
when matrices preserve the Gibbs' phenomenon. In this paper we present a multidimensional extension of the results of Fridy. In particular, we prove necessary and sufficient conditions for a positive RH-matrix to preserve the double Gibbs' phenomenon for positive double sequences. Other related results are also established.

Keywords

double sequence; Pringsheim limit point; P-convergent; RH-regular; P-convergent; Gibbs' phenomenon; double Gibbs' phenomenon

Hrčak ID:

37326

URI

https://hrcak.srce.hr/37326

Publication date:

3.6.2009.

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