Fourier series and the Lubkin W-transform

Abstract

We discuss the effect of a particular sequence acceleration method, the Lubkin W-transform, on the partial sums of Fourier series. We consider a very general class of functions with a single jump discontinuity, and prove that this method fails on a large set of points.

THE $\delta$-SQUARED PROCESS AND FOURIER SERIES OF FUNCTIONS WITH MULTIPLE JUMPS

“…Regrettably, the methods in this paper seem specific to the δ 2 process, so we have not investigated the behavior of series transformed using other algorithms. In [4] the authors show the failure of the Lubkin transform when applied to the Fourier series of a function with one jump. We suspect this holds for functions with multiple jumps, but the computations become unwieldy.…”

Fourier Series Acceleration and Hardy-Littlewood Series

“…Thus, it is desirable to attempt to find methods to speed this convergence. This paper continues investigations began in [1] and [3] to try to determine properties of functions for which one of the sequence acceleration methods described below may accelerate the convergence of its Fourier series.…”