Some properties of the Chebyshev method

Matthew Liu and Billy E. Rhoades

Vol. 80 (1979), No. 1, 213–225

DOI: 10.2140/pjm.1979.80.213

Abstract

Several properties of the Chebyshev method of summability, defined by G. G. Bilodeau, are investigated. Specifically, it is shown that the Chebyshev method is translative and is a Gronwall method. It is shown that the de Vallee Poussin method is stronger than the Chebyshev method, and that the Chebyshev method is not stronger than the (C,1) method. The final result shows that the Chebyshev method exhibits the Gibbs phenomenon.

Mathematical Subject Classification 2000

Primary: 40G99

Milestones

Received: 25 August 1977

Revised: 12 July 1978

Published: 1 January 1979