IJPAM: Volume 88, No. 4 (2013)

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

Emily Jennings$^1$, Charles N. Moore$^2$, Daniel Muñiz$^3$, Ashley Toth$^4$
$^1$Department of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332, USA
$^2$Department of Mathematics
Kansas State University
Manhattan, KS 66506, USA
$^3$Department of Mathematics
University of Florida
Gainsville, FL 32611, USA
$^4$Department of Mathematics
Rollins College
Winter Park, FL 32789, USA


Abstract. We investigate the effects of the $\delta^2$ transform on the partial sums of Fourier series for functions with a finite number of jumps, which in general, converge slowly. Although the $\delta^2$ process is known to accelerate convergence for many sequences, we prove that in this case, the transformed series will usually fail to converge to the original function.

Received: June 9, 2013

AMS Subject Classification: 65B10, 65T40, 42A20

Key Words and Phrases: Fourier series, delta-squared process, convergence acceleration

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DOI: 10.12732/ijpam.v88i4.4 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 4